Two-dimensional Graph Research Articles

Multi-dimensional search for drug–target interaction prediction by preserving the consistency of attention distribution

Predicting drug–target interaction (DTI) is a crucial step in the process of drug repurposing and new drug development. Although the attention mechanism has been widely used to capture the interactions between drugs and targets, it mainly uses the Simplified Molecular Input Line Entry System (SMILES) and two-dimensional (2D) molecular graph features of drugs. In this paper, we propose a neural network model called MdDTI for DTI prediction. The model searches for binding sites that may interact with the target from the multiple dimensions of drug structure, namely the 2D substructures and the three-dimensional (3D) spatial structure. For the 2D substructures, we have developed a novel substructure decomposition strategy based on drug molecular graphs and compared its performance with the SMILES-based decomposition method. For the 3D spatial structure of drugs, we constructed spatial feature representation matrices for drugs based on the Cartesian coordinates of heavy atoms (without hydrogen atoms) in each drug. Finally, to ensure the search results of the model are consistent across multiple dimensions, we construct a consistency loss function. We evaluate MdDTI on four drug–target interaction datasets and three independent compound–protein affinity test sets. The results indicate that our model surpasses a series of state-of-the-art models. Case studies demonstrate that our model is capable of capturing the potential binding regions between drugs and targets, and it shows efficacy in drug repurposing. Our code is available at https://github.com/lhhu1999/MdDTI.

Method of Analysis of the Sample Matching of Diagnostic Ranges of Mineral Nutrients in Soil and Cacao Leaves

ABSTRACT Nutritional diagnostic ranges (NDRs) for soil mineral nutrients (SMNs) and leaf mineral nutrients (LMNs) were obtained from the response of the relative dry biomass of cacao beans (rDBCB) and the relative dry biomass of cacao pod husk (rDBCH). Using an exploratory approach, the sample matching levels of the NDRs were determined to discriminate the results of the soil and leaf nutritional diagnostics. These objectives have been achieved from two methodological processes: a new approach to the boundary line technique where the two-dimensional graph is divided into class intervals based on the predictor variables to then establish the NDR from second degree polynomial regressions, and the development of a classification system for soil and leaf samples by NDR to later verify the corresponding matching levels. This new graphical analysis approach has also allowed us to observe how the SMNs and LMNs present different diagnostic profiles for the prediction of rDBCB and rDBCH responses. The leaf nitrogen (N), potassium (K), magnesium (Mg), and manganese (Mn) concentrations showed an NDR matching level above 80% as predictors of rDBCB and rDBCH responses. Leaf calcium (Ca) concentration showed a level between 60% and 80%. Soil phosphorus (P) concentration showed more than 80% of the sample matching level classified by NDR, followed by the concentrations of K, Ca, and zinc (Zn) in the soil that showed a level of coincidence between 60% and 80%. The lack of uniformity in the genetic potential of cacao production and management has produced differences between predictions.

Exploring dynamic behaviors of soliton-like pulses in the lossy electrical transmission line model with fractional derivatives: A comparative study

This study aims to explore the intricate behavior of soliton-like pulses within a nonlinear and lossy electrical transmission line. The transmission line is described by a mathematical model called the “beta derivative”, which is specifically designed to characterize the propagation of electrical solitons in media with both nonlinearity and dispersion properties. To achieve this goal, the (G′/G2)-expansion method is applied to a periodically loaded nonlinear beta derivative lossy transmission line with symmetric voltage-dependent capacitances. Soliton-like pulses, including periodic singular, dark, bright, and singular waves, are obtained using the (G′/G2)-expansion method based on the voltage equation. Three-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying relevant equations are provided to understand the underlying mechanisms of the soliton family. In terms of fractionality, the profiles of dark or bright waveforms maintain their complete forms, but their smoothness increases as the fractional parameters increase. On the other hand, periodic wave solutions exhibit an increase in periodicity. By adjusting the parameters of the model, the characteristics of the waves can be modified to generate desired wave profiles. Additionally, the study involves a comprehensive comparison among solutions derived from models incorporating the beta, conformable, and M−truncated derivatives. It examines how the amplitude of the solitons is influenced by the fractional parameter, utilizing graphs to visualize this impact by assigning specific fractional parameter values. These pulse-like solitons offer promising potential for integration within telecommunication systems, where they can function as information carriers, facilitating heightened data bit rates. By leveraging the findings of this study, advancements in telecommunication technology can be pursued, leading to enhanced efficiency and improved performance.

Зависимость величины сигнала от смещения кружка рассеяния объектива в диапазоне углов 0º - 90º относительно центра пиксела фоточувствительной матрицы

An algorithm has been developed for calculating the change in the irradiation level of a matrix pixel when the focal spot shifts relative to the center of the matrix pixel in the range from 0 ° to 90 °. Two types of pixel irradiance distribution are considered: distribution in the lens scattering circle in the form of a gaussian rotation and uniform irradiance. Method. The calculation is based on the method of dividing the lens scattering circle on the matrix pixel into separate areas, according to which the irradiance is calculated. The displacement of the lens scattering circle by ∆x along the X axis and by ∆y along the Y axis is taken as normalized to the spot radius. To create a two-dimensional graph of the dependence of the pixel irradiance on the displacement of the lens scattering circle along the X, Y axes, we introduce the transformed relative displacement of the lens scattering circle γ. The main results. An algorithm has been developed for calculating the change in the irradiation level of a matrix pixel when the lens scattering circle is shifted relative to the matrix pixel for two cases of pixel irradiation: the distribution in the lens scattering circle in the form of a gaussian rotation and uniform irradiation. The dependence of the normalized irradiance of the matrix pixel on the transformed relative displacement of the lens scattering circle γ at an angle of 0 °, 30 °, 45 °, 60 °, 90 ° is plotted on the graph for the above cases of irradiation.

Comparative effectiveness and safety of 36 therapies or interventions for pregnancy outcomes with recurrent implantation failure: a systematic review and network meta-analysis.

To investigate the effectiveness and safety of 36 different therapies for recurrent implantation failure (RIF) patients. We searched PubMed, Embase, the Cochrane Library (CENTRAL), Web of Science, and China National Knowledge Internet (CNKI) from inception to August 24, 2022, with language in both English and Chinese. Randomized controlled trials (RCTs) and observational studies that provided data with one of pregnancy outcomes on RIF patients were included in the network meta-analysis (NMA). The odds ratios (OR) and 95% credible interval (CrI) on pregnancy outcomes were summarized by NMA with a random-effects model. We also analyzed data from only RCTs and compared whether the optimal treatment is the same for different failed embryo transfer attempts. The total of 29,906 RIF patients from 154 clinical studies (74 RCTs and 80 non-RCTs) were included in the NMA. In terms of implantation rate (IR), growth hormone (GH) (OR: 3.32, 95% CrI: 1.95-5.67) is the best treatment in all included studies; IVIG+PBMC (5.84, 2.44-14.1) is the best for clinical pregnancy rate (CPR); hyaluronic acid (HA) (12.9, 2.37-112.0) for live birth rate (LBR); and aspirin combined with glucocorticoids (0.208, 0.0494-0.777) for miscarriage rate (MR). The two-dimensional graphs showed that GH could maximize IR and CPR simultaneously; HA and GH could simultaneously increase IR and LBR to a large extent; HA could maximize IR and minimize MR. IVIG+PBMC, GH, and embryo medium enriched with HA could significantly improve pregnancy outcomes in patients with RIF. It appears that combination therapy is a potential administration strategy. This study has been registered on PROSPERO (CRD42022353423).

Spatial evaluation and zoning strategy of land use elemental conflicts in heavy industrial zones: evidence from central Liaoning Province in Northeast China.

The matching imbalance of resource factors leads to land use elemental conflicts (LUECs), which has become the bottleneck restricting high-quality social and economic development. The heavy industrial zones (HIZ) have become the focus area of LUECs due to the high-resource consumption. Taking the urban group of central Liaoning Province, the area of industrial revitalization in northeast China as a case study area, the study proposed a wavelet coherence approach to identifying the influencing indicators and indicators weight of LUECs for spatial evaluation. Two-dimensional graph theory is used to cluster the evaluation results of LUECs at the plot scale and controls the main indicators to put forward the zoning strategies of LUECs. The results showed that the main indicators affecting LUECs in the western part of the HIZ are mainly human indicators, while the fierce conflicts in the east mainly come from natural indicators. The zoning strategies of LUECs in the HIZ should prevent excessive energy consumption from increasing carbon emissions in intense conflict zone and moderate conflict zone and strengthen the rural settlement arrangement and soil erosion control in mild conflict zone and structure ecological security early warnings in potential conflict zone. This study provides an important reference for land use conflicts in the global heavy industrial urban agglomeration.

Exploring Families of Solitary Wave Solutions for the Fractional Coupled Higgs System Using Modified Extended Direct Algebraic Method

In this paper, we suggest the modified Extended Direct Algebraic Method (mEDAM) to examine the existence and dynamics of solitary wave solutions in the context of the fractional coupled Higgs system, with Caputo’s fractional derivatives. The method begins with the formulation of nonlinear differential equations using a fractional complex transformation, followed by the derivation of solitary wave solutions. Two-dimensional, Three-dimensional and contour graphs are used to investigate the behavior of traveling wave solutions. The research reveals many families of solitary wave solutions as well as their deep interrelationships and dynamics. These discoveries add to a better understanding of the dynamics of the fractionally coupled Higgs system and have potential applications in areas that use nonlinear Fractional Partial Differential Equations (FPDEs).

Cost-effectiveness analysis of transplant-ineligible relapsed or refractory diffuse large B-cell lymphoma treatment options-Experience of the efficiency frontier approach.

The treatment of relapsed/refractory (R/R) diffuse large B-cell lymphoma (DLBCL) changed remarkably since the European Medicines Agency-approved chimeric antigen receptor T-cell (CAR-T) therapies (axicabtagene ciloleucel [axi-cel], lisocabtagene maraleucel [liso-cel], tisagenlecleucel [tisa-cel]) for the third-line onwards (3+L), and targeted therapies (polatuzumab vedotin-bendamustine-rituximab [pola-BR], tafasitamab-lenalidomide [Tafa-L]) for the second-line (2L) onwards. As associated rising treatment costs represent an economic burden, the cost-effectiveness of transplant-ineligible R/R DLBCL interventions was assessed from a German healthcare payer's perspective, using the efficiency frontier (EF) approach. A systematic literature review was performed to determine the clinical benefit concerning median overall survival (OS) of bendamustine-rituximab (BR), rituximab-gemcitabine-oxaliplatin (R-GemOx), axi-cel, liso-cel, tisa-cel, pola-BR, and Tafa-L. First-year treatment costs (drug and medical services costs) were calculated. Results were merged on two-dimensional graphs illustrating 2L and 3+L EFs. Second-line EF is formed by BR (median OS 11.49 months, €23 958) and Tafa-L (45.7, €104 541), 3+L EF is formed by R-GemOx (12.0, €29 080), Tafa-L (15.5, €104 541), and axi-cel (18.69, €308 516). These interventions build the respective cost-effectiveness thresholds for novel interventions. Using the EF approach, the currently most cost-effective interventions (based on cost-effectiveness ratios) in the indication of R/R DLBCL were identified to guide international reimbursement decisions.

Preliminary application of three-dimensional venography and fusion navigation technique in May-Thurner syndrome

ObjectiveThe purpose of this study was to report a technique for intraprocedural guidance of endovascular iliac vein stenting procedures using three-dimensional (3D) venography images as an overlay on live biplanar fluoroscopy. MethodsUsing 3D venography and a fusion navigation technique, percutaneous transluminal angioplasty and stent placement were performed to evaluate the feasibility of using 3D venography images and the fusion navigation technique to treat MTS compared with traditional digital subtraction angiography. The general epidemiologic data (ie, age, gender), clinical manifestations (ie, major symptoms, affected extremity, CEAP [clinical, etiology, anatomy, pathophysiology] classification, comorbidity, stenosis rate), intraoperative findings (ie, stent type, stent count, stent to inferior vena cava distance, procedure time, radiation dose, contrast agent dosage), and postoperative recovery were obtained and analyzed. ResultsA total of 30 consecutive patients with symptomatic MTS from our institution were enrolled in the present study. Of the 30 patients, 12 (group A) were treated using 3D venography images and fusion navigation and 18 (group B) were treated with two-dimensional venography images during endovascular management. Significant differences were observed between the two groups with respect to the procedure time (64.42 ± 4.35 minutes vs 76.61 ± 3.47 minutes; P = .04), radiation dose (2152 ± 124.7 mGy vs 2561 ± 105.6 mGy; P = .02), and contrast agent dosage (71.42 ± 4.87 mL vs 86.17 ± 4.14 mL; P = .03). Conclusions3D venography and its fusion navigation technique can improve prediction of the coverage area of the stent. Its use can also shorten the procedure time and reduce the contrast agent dose and radiation exposure, making it a valuable tool for both the diagnosis and the treatment of symptomatic MTS.

New traveling solutions, phase portrait and chaotic pattern for the generalized (2+1)-dimensional nonlinear conformable fractional stochastic Schrödinger equations forced by multiplicative Brownian motion

The paper mainly studies the traveling wave solutions, phase portrait and chaotic pattern of the generalized fractional stochastic Schrödinger equations forced by multiplicative Brownian motion. By using the polynomial complete discrimination method, the hyperbolic functions, rational functions and Jacobi elliptic function solutions are obtained. Moreover, the physics properties of the obtained solutions are shown through three-dimensional, two-dimensional and contour graphs. In order to help better analyze dynamic behavior, phase diagrams, chaos behavior and sensitivity are plotted by using Maple software.

Fine-Gained Recurrence Graph: Graphical Modeling of Vibration Signal for Fault Diagnosis of Wind Turbine

Benefiting from the recent successes of convolutional neural networks (CNNs), many studies have modeled the vibration signal of energy system into a two-dimensional (2D) input graph to amplify and highlight fault features. However, most works seldomly consider the system dynamic characteristics, which may affect the knowledge discovery and diagnosis quality. To address this issue, this paper proposes a novel graphical modeling approach, termed as fine-gained recurrence graph (FRG), to capture dynamic characteristics of vibration signals from the view of nonlinear dynamics. FRG focuses on modeling the temporal correlations and tendencies between state vectors in phase space and then visualizes the characteristics to represent intrinsic dynamic changes of the vibration signals into 2D graphs. The information representation capability of the proposed FRG is verified using different dynamic signals. Based on this finding, an ensemble fault diagnosis model is proposed fusing FRG with deep CNNs. Meanwhile, transfer learning is accompanied to deal with the training difficulties of deep CNNs. Finally, case studies on experimental data and real wind turbine data illustrate its effectiveness and feasibility. Comparisons with four state-of-the-art approaches have confirmed the preferable information representation and diagnosis performance of the proposed approach.

A polynomial of degree five representing the selling price of an inventory of deteriorating items with a linear degradation rate, constant holding cost, and demand-dependent selling price

The study suggests a deterministic inventory model as opposed to a probabilistic one. With just odd powers considered, the model's demand rate is a degree five polynomial of the selling price. The keeping expense is assumed to stay constant. Time has an impact on how quickly things degrade. The backlog and shortages are both acceptable. The inventory model used a single article inventory. It is assumed that there is no lead time. In this study, the differential equation's solution was used to determine the best values. The model is numerically validated, and in a maple application, convexity is displayed as a two-dimensional graph.

A study on soliton, lump solutions to a generalized (3+1)-dimensional Hirota--Satsuma--Ito equation

Abstract In this article, through the Hirota bilinear method and long wave limit method, based on the N-solitons, we construct the multiple lump solutions of the generalized (3+1)-dimensional Hirota–Satsuma–Ito equation. Furthermore, to enhance our understanding of the solutions obtained, we further elucidate the physical implications of these solutions with three-dimensional and two-dimensional graphs. The solutions obtained might have practical applications in elucidating the dynamic behaviors of higher-dimensional systems, particularly in the study area of waves in shallow water and the study of nonlinear optics.

An Analytical Study on Soil Water Index (SWI), Landslide Prediction and Other Related Factors Using XRAIN Data during the July 2018 Heavy Rain Disasters in Hiroshima, Japan

The rainfall-induced landslide disasters in July 2018 in Southwestern Japan yet again exemplified the severity of slope failure-related damage and the need for improvement of early warning systems. The Japanese Meteorological Agency (JMA) uses a method based on a threshold value of soil water index (SWI), a conceptual measurement that represents saturation of slope soil. The current SWI early warning system uses 60-min rainfall data on a 5-km2 mesh and does not take into consideration other landslide conditioning factors such as slope angle and geology. This study calculates SWI values during the July 2018 disasters in Kure City (Hiroshima Prefecture) using 1-min XRAIN rainfall data in a 250-m mesh to investigate the relationship between SWI and landslide occurrence. It was found that the SWI threshold of 124 mm used in the JMA early warning system for the area was surpassed in all cells. A new SWI threshold calculation method taking slope angle and geology into consideration and produced with machine learning is proposed, comprising power lines for different geological units at a two-dimensional graph where points located above the threshold line represent landslide risk. It is judged that this method would provide a more accurate early warning system for landslide disasters.

Cost-Effectiveness Analysis of Biologics in the Treatment of Moderate-to-Severe Plaque Psoriasis from a Health Care Provider's Perspective

Introduction: Psoriasis (psoriasis) is a chronic disease with a number of significant comorbidities and often with a very significant impact on the quality of life of patients. Recently, a relatively large number of biological treatment products with a significant effect have entered the market, but they are also significantly more expensive than systemic conventional treatment. In the context of the published long period of inadequate treatment of patients with psoriasis in the Czech Republic, the health care system and the limited costs of center drugs, it is necessary to make the greatest possible effort at the level of the provider of this health care to effectively spend financial resources and provide highly effective treatment to the greatest possible number of patients. Method: With a model-set amount of the unit prices of the packaging of preparations according to the maximum reimbursements in the Czech Republic in 2021, a fictitiously set amount of bonuses for only two selected preparations (this is a model example that does not reflect the real state of business policy at the University Hospital Olomouc), and the conditions for reimbursement of biological treatment preparations psoriasis in the Czech Republic in 2021, a cost-effectiveness analysis (CEA) was carried out in the selected PASI 100 efficiency parameter. The analysis was carried out and processed interactively in the Excel software into the graphical form of the outputs, especially in the form of forest plot graphs (in the CER and ICER parameters) and in a two-dimensional efficient frontiers graph (costs vs. efficiency). Results: The differences in the cost-effectiveness of individual preparations according to the point values of the CER and ICER parameters are up to several times. Taking into account the 95% confidence intervals, some of the differences between the preparations are also statistically significant. With the most cost-effective sequence of treatment for a gradually more effective drug in one patient during the induction period of treatment, we can, based on the saved costs, start induction treatment with a less effective biologic in two more patients than when using the second cost-effective sequence of treatment escalation. Conclusion: The cost-effectiveness analysis (CEA) of biological drugs in the treatment of psoriasis at the level of the health service provider has great potential in the effort to make the treatment as effective as possible with limited financial resources, or in the effort to provide effective treatment to additional patients with the same limitations

A Content Analysis of Tasks Involving Two-Dimensional Cartesian Graphs in Grade 6–8 U. S. Textbooks

ABSTRACT Understanding and supporting students’ development of graph literacy is important. We studied how aspects of graph literacy might be supported (or hindered) in middle school by analyzing the content in textbooks. Specifically, we conducted a content analysis of tasks involving two-dimensional Cartesian graphs presented in grade 6–8 US textbooks. Three elements were analyzed: the type of activity involved in graphing, the nature of the graph, and the relevant mathematical topic. We first present three illustrative tasks to demonstrate how we made sense of these three elements with graphing tasks. Second, we present the frequency of different types of coordinate system activity, graph activity, and coordinate system types involved in textbook tasks and how they change across grade level and mathematical domain. Our findings reveal varying levels of explosure to different graphing elements students might encounter through textbooks. We discuss implications of our findings on research, teaching, and curriculum development.

Determination of the Boundaries of Changes in External Parameters that Complicate the Calculation of the Suspension of Agricultural Machinery

Introduction. The article deals with the problem of calculating the strength of the shaft of the wheel drive of agricultural machinery. The strength conditions of both the maximum torque and the values of relative deformations of the shaft are taken into account. Aim of the Article. Of the research is to determine the limits of external influences on a structural element, caused by the distributed weight of the motor-tractor machinery, at which it is necessary to construct not only the torque and strain diagrams, but also to determine the extreme values at each section, where the strength index of the structure is nonlinear. Materials and Methods. In calculations, the main provisions of continuum mechanics, theory of machines and mechanisms, as well as the basics of design in mechanical engineering are used. Central attention is paid to the influence of external influencing factors on the character of internal force distribution in the shaft. Results. The obtained area of variation of parameters P-q allows us to determine the necessity of more detailed calculation of strength parameters of the considered part. This is due to the emergence of extreme areas outside the boundaries of individual areas of consideration of the shaft work. The results are presented as a two-dimensional graph of the ratio of external influences, at which the specified effect takes place. Discussion and Conclusion. In comparison with typical calculations, regulated by normative documents, the proposed algorithm at the preliminary stage allows to determine the cases when nonlinear regions of bending moment changes require additional investigations. The use of the proposed algorithm allows, without resorting to time-consuming numerical methods of calculating the strength indicators of a wheel drive shaft, such as the finite element method, to obtain a more detailed picture of the nature of distribution of internal forces and deformations in the part under study.

Analysis of the gains and losses of ecosystem service value under land use change and zoning in Qiqihar

Under a background of uncoordinated economic development and the ecological environment, quantifying the ecological effect brought by land resource changes, have become research key and hotspots. To explore land use change and its impact on ecosystem service value (ESV), the land use change analysis method, ecosystem service evaluation model, flow direction analysis model and two-dimensional graph theory clustering method were used to analyze the profit and loss of ESV in Qiqihar in 2010 and 2020 and the division of ecological function areas with counties as units. The results show that: 1) The land use change in Qiqihar city is more obvious, Among them, the area of cultivated land, wetland, construction land and other increases, Woodland, grassland, water area decreased, The changed land area accounts for 30.95% of the total area; 2) The ESV in Qiqihar city increased by 869 million yuan, The sum of the value of cultivated land and wetland exceeded 70.0% of the ESV, is the main source of ESV in Qiqihar city; 3) Not all land-use shifts are conducive to ESV growth. The increase of ESV mainly comes from the flow of cultivated land and grassland to the wetland; Conversion of woodlands, water area, wetlands to other types causes ESV loss, the most loss is the conversion of wetlands to cultivated land; 4) Qiqihar city is divided into the central wetland ecological conservation area, the western characteristic agriculture and dotted wetland ecological function area, and the northeast agricultural ecological environment construction functional area. Three policies were proposed to improve ESV:(1) give play to the radiation role of wetland nature reserves; (2) popularize the black land protection technology model; and (3) prevent and control agricultural non-point source pollution and promote clean agriculture.

Diversity of soliton solutions to the (3 + 1)-Dimensional Wazwaz-Benjamin-Bona-Mahony equations arising in mathematical physics

The current study scrutinizes exact singular solitary, kink, anti-kink, bell-shaped, and periodic traveling wave solutions for the newly implemented 3-dimensional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations family using a modified Exp-function approach. In spite of the presence of several trigonometric, hyperbolic, and rational functions, some new exact solitary, hyperbolic, and periodic traveling wave solutions to the considered equations are obtained by putting the modified Exp-function method into practice using the computer program Maple. The arrangement of the functions tanh, sech2, tan, and sec2 expresses the specific solutions produced by the defined procedure. The information was obtained to evaluate how well the suggested method could compute the exact solutions of the WBBM equations that could be applied to nonlinear water model applications in the ocean and coastal engineering. To show the physical composition and properties of the discovered solitons, contour, three-, and two-dimensional graphs are plotted using the computer program Mathematica. The acquired results imply that the proposed method can be applied to find various, enhanced, useful, and compatible solutions for other important nonlinear partial differential equations. All of the solutions given have been qualified by swapping the respective equations with those generated via the computer program Maple. Furthermore, we compared our obtained results with the solutions already put forward in the literature.

Dynamics and optical solitons in polarization-preserving fibers for the cubic–quartic complex Ginzburg–Landau equation with quadratic–cubic law nonlinearity

In this paper, the cubic–quartic complex Ginzburg–Landau (CGL) equation is investigated by using the trial function method. The traveling wave hypothesis is applied to convert the CGL equation to an ordinary differential equation (ODE), which is equivalent to a dynamic system. The qualitative behavior, bifurcation of the phase portraits for this system is studied. Furthermore, the chaotic motions in system involving external periodic perturbation are considered. Some new optical solitons, such as Jacobian elliptic function solutions, for CGL equation with quadratic–cubic law nonlinearity are constructed using the complete discrimination system for polynomial method. Moreover, two-dimensional graphs, three-dimensional, corresponding contour and density plots for some acquired solutions are depicted to carry out the physical properties of optical pulse propagation.