Spatio-temporal Dispersions Research Articles

Optical soliton solution of the perturbed Fokas–Lenells equation having the cubic–quintic–septic law of self-phase modulation in the presence of chromatic and spatiotemporal dispersions

Optical soliton solution of the perturbed Fokas–Lenells equation having the cubic–quintic–septic law of self-phase modulation in the presence of chromatic and spatiotemporal dispersions

Optical soliton solution of the perturbed Biswas-Milovic equation having cubic-quintic-septic law nonlinearity in the presence of spatio-temporal and chromatic dispersion

In this manuscript, we investigate the analytical and soliton solutions of the cubic-quintic-septic law for the perturbed Biswas-Milovic equation, considering spatio-temporal and chromatic dispersions. The perturbed Biswas-Milovic equation with the spatio-temporal and chromatic dispersion terms provides a comprehensive study for describing nonlinear optical wave propagation in optical fiber. We use the wave transformation to reduce the main equation to a nonlinear ordinary differential equation. The transformation of the original equation into a more simplified form aims to attain a more profound comprehension of the fundamental dynamics of the system. We retrieve the analytical solutions of the presented model by implementing the new Kudryashov technique and a subversion of the new extended auxiliary equation approach. Besides, bright, singular, and V-shape soliton structures are represented. By employing powerful analytical techniques, we systematically derive a wide range of soliton solutions. This approach successfully captures diverse soliton types highlighting the novelty of applying the new Kudryashov technique and a subversion of the new extended auxiliary equation method to this complex model. Moreover, we analyze the soliton behavior influenced by various parameters. The analysis of the parameter influences reveals the complicated relationship governing the dynamics of the perturbed Biswas-Milovic model. Furthermore, this manuscript includes the modulation instability analysis for the presented model. Conducting modulation instability analysis for the presented equation enhances our understanding of the system’s stability and dynamics.

Bright soliton of the third-order nonlinear Schrödinger equation with power law of self-phase modulation in the absence of chromatic dispersion

In this article, we are interested in two principal topics. First, the bright optical soliton solutions of the third-order (1+1)-nonlinear Schrödinger equation including power law nonlinearity with inter-modal and spatio-temporal dispersions are perused by taking advantage of the new Kudryashov method. Second, the impacts of power law nonlinearity parameters on soliton attitude are investigated for acquired bright soliton form. With the proposed technique, the bright optical soliton solution is acquired, and 3D, contour, and 2D plots are depicted. Then, the impact of power law nonlinearity parameters on the soliton attitude has been successfully demonstrated. As is clear from this perusal power law parameters have an important impact on the soliton attitude, and this impact alters based on the soliton form. As regards our investigation, this form of the equation has not been studied with the power law nonlinearity in the absence of the chromatic dispersion for nonlinear models and the proposed method has not been applied the introduced equation before. It is expected that the consequences which are acquired in this study will shed light on the studies in this field.

First clinical data on artificial intelligence-guided catheter ablation in long-standing persistent atrial fibrillation.

Despite advanced ablation strategies and major technological improvements, treatment of persistent atrial fibrillation (AF) remains challenging and the underlying pathophysiology is not fully understood. This study analyzed the multiple procedure outcome and safety of catheter ablation of spatiotemporal dispersions (DISPERS) detected by artificial intelligence (AI)-guided software in patients with long-standing persistent AF. The Volta VX1 software was used for 50 consecutive patients undergoing catheter ablation for persistent AF. First, high-density mapping (78% biatrial) with a multipolar mapping catheter was performed. In addition to pulmonary vein isolation (PVI), ablation of DISPERS was performed aiming at homogenizing, dissecting, isolating, or connecting DISPERS areas to nonconducting anatomical structures. Follow-up contained regular visits at our outpatient clinic at 1, 3, 6, and 12 months including 7-day Holter electrocardiograms. Patients were mainly suffering from long-standing persistent AF (mean AF duration 50.30 ± 54.28 months). Following PVI, ablation of left atrial and right atrial DISPERS areas led to AF cycle length prolongation (mean of 162.0 ± 16.6to 202.2 ± 21.6 ms after) and AF termination to atrial tachycardia (AT) or sinus rhythm (SR) in 12 patients (24%). No stroke or pericardial effusion occurred; major groin complications (pseudoaneurysm n = 1, atrioventricularfistula n = 1) were detected in two patients. After a blanking period of 6 weeks, recurrence of any atrial arrhythmia was documented in 26 patients (52%). The majority of patients presented with organized AT (n = 15) while AF was present in n = 9 patients and AT/AF was observed in n = 2 patients. Twenty-twopatients underwent reablation. During a mean follow-up of 363.14 ± 187.42 days and after an average of 1.46 ± 0.68 procedures, 82% of patients remained in stable SR. DISPERS-guided ablation using machine learning software (the Volta VX1 software) in addition to PVI in long-standing persistent AF ablation resulted in high long-term success rates regarding AF and AT elimination. Most arrhythmia recurrences were reentrant AT. After a total of 1.46 ± 0.68 procedures, freedom from AF/AT was 82%. Despite prolonged procedure times complication rates were low. Randomized studies are necessary to evaluate long-term efficacy of dispersion-guided ablation using AI.

Investigating of the pure-cubic optical solitons in the presence of spatio-temporal and inter-modal dispersions

Investigating of the pure-cubic optical solitons in the presence of spatio-temporal and inter-modal dispersions

Construction of chirped propagation with Jacobi elliptic functions for the nonlinear Schrödinger equations with quadratic nonlinearity with inter-modal and spatio-temporal dispersions

Construction of chirped propagation with Jacobi elliptic functions for the nonlinear Schrödinger equations with quadratic nonlinearity with inter-modal and spatio-temporal dispersions

Highly dispersive solitons in polarization-preserving fibers by Adomian decomposition method

This paper numerically studies the existence and characteristics of highly dispersive bright optical solitons in polarization-preserving fibers. The numerical strategy adopted here is the Adomian decomposition method (ADM). The governing model is without self-phase modulation as its influence is negligible. We consider the impacts of group velocity dispersion, third-order dispersions, spatiotemporal dispersion, and nonlinear dispersions on the evolution of bright soliton. We have numerically obtained the bright soliton, which is formed as a result of robust balance among linear and nonlinear temporal as well as spatiotemporal dispersions. To check the accuracy of our numerical results we compare them with the analytical solution. The absolute error is very small and negligible even at large values of propagation time.

Optical soliton solutions of the stochastic perturbed Radhakrishnan-Kundu-Lakshmanan equation via Itô Calculus

This study presents, for the first time, optical solitons of the stochastic perturbed Radhakrishnan-Kundu-Lakshmanan equation with Kerr law nonlinearity in the presence of chromatic and spatio-temporal dispersions. The stochastic form involves multiplicative white noise in the Ito sense, besides; the Kudryashov and the new Kudryashov methods are picked to analyze. The analysis of the stochastic soliton solutions of the Radhakrishnan-Kundu-Lakshmanan equation and the impact of noise on these solitons are the primary motivations for choosing both of these techniques rather than obtaining many solitons. Therefore, the first goal is to obtain the most basic soliton types, bright and dark solitons, and the second goal is to observe the white noise effect on these solitons. By applying the proposed methods, bright and dark solitons are obtained, and the noise effect on these solitons is illustrated using both 3D and 2D graphic presentations, along with necessary comments. The presentation of the examined model for the first time in this article reflects its originality in terms of contributing both the study and the obtained results to the literature.

Targeted ablation of arrhythmogenic substrate in complex cases of very long-standing persistent atrial fibrillation: successful ablation of spatio-temporal dispersions

Abstract Funding Acknowledgements Type of funding sources: None. Introduction In persistent AF, outcomes after PVI alone is worse as the pathophysiology remains unclear. Prolonged AF duration is an independent predictor for worse success rates after catheter ablation. In this study, we investigated efficacy and safety of ablation of spatio-temporal dispersions, as additional ablation strategy after PVI in patients with long-standing persistent AF. Methods All consecutive patients with long-standing persistent AF treated with an AI-based algorithm for detection of spatio-temporal dispersion in our institution between 05/21 and 10/22 were included (n = 41, see table 1). The procedure was done using a high-density 3D-Map and an algorithm for detection of right and left atrial areas with spatio-temporal dispersion (DISPERS). Ablation of DISPERS was aiming at homogenizing, dissecting, isolating or connecting DISPERS areas to non-conducting structures. Follow-up contained regular visits at our out-patient-clinic and repetitive 7 day Holter ECGs. Late recurrence (LR) was defined as recurrence after 90 days or as recurrence, which caused further ablation. All complications requiring intervention or causing long-term sequelae were classified as major complications. Results In 24/41 pts (58.5%), the DISPERS guided ablation was the first AF ablation. Patients were suffering from very long-standing persistent AF with a mean AF duration of 64.89 ± 54.77 months. Additional to circumferential PVI, ablation of all detected left atrial (100%) and right atrial (68.3%) DISPERS areas was performed, leading to significant slowing of AF cycle length (mean 23.3%) or termination of AF to AT (5/41, 12.2%) or direct conversion to SR (6/41, 14.6%). One major complication occurred (1/41 (2.4%), pseudoaneurysm, resolving after manual compression). Three patients (7.3%) required temporary external pacing due to delayed sinus recovery after the procedure. No patient was in need of permanent pacemaker implantation. LR occurred in 25 patients (61.0 %): In 8/25 patients (32 %), LR was solely AF, whereas in 15/25 patients (60%) LR was a left AFlutt. In 2 patients (8%), AF and left AFlutt was detected. During a follow-up of 231 ± 129 days, 72.9 % of patients remained in sinus rhythm undergoing 1.6 ± 0.68 ablations (s. Figure 1; 4,9% of patients on AAD). Additionally, Figure 2 illustrates the AF-free outcome in all patients. Conclusion Ablation of arrhythmogenic substrate identified by spatio-temporal dispersion yielded in this cohort of extensively long-standing persistent AF patients in high success rates regarding elimination of AF. Most arrhythmia recurrences were reentrant AT. After a total of 1.6 procedures, freedom from AF and AT was >72%. Despite prolonged procedure times, complication rates remained very low. Extending study population and follow-up is needed to evaluate long-term efficacy of dispersion-guided ablation.

Optical solitons and conservation laws for the concatenation model with spatio-temporal dispersion (internet traffic regulation)

This paper presents optical solitons with the concatenation model having spatio-temporal and chromatic dispersions. This model can advantageously curtail the Internet bottleneck effect. Two integration schemes yield these solitons. By utilizing the multipliers approach, the conservation laws are also derived.

Dispersive Optical Solitons to Stochastic Resonant NLSE with Both Spatio-Temporal and Inter-Modal Dispersions Having Multiplicative White Noise

The current article studies optical solitons solutions for the dimensionless form of the stochastic resonant nonlinear Schrödinger equation (NLSE) with both spatio-temporal dispersion (STD) and inter-modal dispersion (IMD) having multiplicative noise in the itô sense. We will discuss seven laws of nonlinearities, namely, the Kerr law, power law, parabolic law, dual-power law, quadratic–cubic law, polynomial law, and triple-power law. The new auxiliary equation method is investigated. We secure the bright, dark, and singular soliton solutions for the model.

The bright and singular solitons of [formula omitted]-dimensional nonlinear Schrödinger equation with spatio-temporal dispersions

The primary goal of this paper is to investigate the bright and singular solitons of (2+1)-dimensional improved nonlinear Schrödinger equation with spatio-temporal dispersions, group-velocity dispersions, and power law nonlinearity. This important goal is achieved by using the Kudryashov method (KM), a complex transformation as well as symbolic computations. As a result, we achieve several constraint conditions that guarantee the existence of soliton solutions. Graphical plots are used to explain the effect of various physical parameters on the solutions. All the results demonstrate the proposed method is stable, reliable, and accurate.

Optical solitons of (2 + 1)-dimensional nonlinear Schrödinger equation involving linear and nonlinear effects

The main purpose of the present paper is to study a (2+1)-dimensional nonlinear Schrödinger equation (2D-NLSE) involving group-velocity dispersions, spatio-temporal dispersions, and the Kerr law nonlinearity. Such a key goal is accomplished by applying a complex transformation and the new Kudryashov method with the help of symbolic computations. As an achievement, several optical solitons to the 2D-NLSE in the presence of linear and nonlinear effects are formally retrieved.

Chirp-free optical dromions for the presence of higher order spatio-temporal dispersions and absence of self-phase modulation in birefringent fibers

In this paper, we study Biswas–Arshed (BA) model in birefringent fibers for chirp-free solitons (dromions) with the aid of sub-ordinary differential equations (ODE) method. The BA model studies the soliton transmission in optical fiber. We obtain bright, periodic, and Weierstrass elliptic function solutions with constraint conditions.

Stochastic treatment of the solutions for the resonant nonlinear Schrödinger equation with spatio-temporal dispersions and inter-modal using beta distribution

In this paper, the extended Jacobian elliptic function expansion method is implemented in order to construct some new traveling wave solutions for the resonant nonlinear Schrodinger equation with both spatio-temporal dispersion and inter-modal dispersion. These new traveling wave solutions are obtained by the proposed method, which is easy to implement and computationally very attractive. Moreover, these solutions may be applicable for some physical fields, such as plasma physics. The main aim of this paper is the stochastic treatment of the solutions when the spatio-temporal coefficient or the wave transition is beta random variables. The priority of using beta statistical distribution for the spatio-temporal is discussed. Some graphical simulations are given to illustrate the behavior of these solutions in the deterministic and stochastic case studies. Indeed the proposed techniques are very powerful tool to solve other models in applied science.

Optical travelling wave solutions for the Biswas–Arshed model in Kerr and non-Kerr law media

This paper scrutinises the newly proposed Biswas–Arshed model for soliton propagation through optical fibres, with small group velocity dispersion and in the absence of self-phase modulation. Spatio-temporal dispersions of higher order are considered to balance with group velocity dispersion. First integral and functional variable methods are employed to recover solitary wave, shock wave, singular wave and singular periodic wave solutions for the two nonlinear forms of the model through Kerr law and power-law nonlinearity. The constraint relations are also figured for the manifestation of these optical solutions.

New optical solitons of Biswas-Arshed equation using different techniques

This paper scrutinizes the newly proposed Biswas-Arshed equation with Kerr and power law nonlinearities for soliton propagation through optical fibers, with small group velocity dispersion and in absence of self-phase modulation. Spatio-temporal dispersions of higher order are considered in compensation with group velocity dispersion. In this work, bright, dark, singular and bright-singular combo soliton solutions are retrieved using undetermined coefficients and Kudryashov's methods.

Instabilities and solitons in systems with spatio-temporal dispersions and non paraxial approximations

We consider the evolution of light beams in nonlinear Kerr media wherein the beam propagation is governed by the coupled non-paraxial (2+1) dimensional nonlinear Schrödinger equation. In the advent of system failing to obey the slowly varying envelope approximation, the usual paraxial approximation cannot be adopted. Our model equation could potentially serve as a governing model for nano-waveguides and on-chip silicon photonic devices. Using the trial solution method, we derive the different combinations of soliton solutions such as bright–bright, dark–dark, and bright–dark soliton and briefly discuss the characteristics of the soliton. Following the initial discussion on the soliton solution, we extend the study to investigate the modulational instability of the system of equations. We examine the role of the dispersion/diffraction in the instability spectra and demonstrate the different characteristics of the instability bands as a function of system parameters.

W-shaped, bright and dark solitons of Biswas–Arshed equation

We investigate the new model proposed by Biswas and Arshed which applies for soliton transmission through optical fibers where self-phase modulation is totally absent. For the low group velocity dispersion to be compensated, both spatio-temporal dispersions of second- and third-order are included in the model. A class of solitary wave solutions of the W-shaped, bright and dark type are obtained by adopting a complex amplitude ansatz solution. The conditions on the fiber parameters for the existence of these structures are also reported. Our results may raise the possibility of some experiments and potential applications related to optical fiber systems in the in presence of higher-order dispersions and absence of cubic nonlinearity.

Optical solitons in presence of higher order dispersions and absence of self-phase modulation

This paper proposes a new model for soliton transmission through optical fibers where self-phase modulation is negligibly small and hence removed. The model however includes spatio-temporal dispersions, of second and third order, to compensate for low group velocity dispersion. The balance for sustaining solitons is provided by nonlinear dispersion terms that are considered in this model.