Soliton solutions and chaotic structures of a (2+1)-dimensional nonlinear electrical network system

Solitons for the (2 + 1)-dimensional Konopelchenko–Dubrovsky equations

Temporal behavior of bright and dark spatial solitons in photorefractive crystals having both the linear and quadratic electro-optic effects based on low amplitude approximations

Soliton dynamics and nonlinear phenomena in quantum deformation has been investigated through conformal time differential generalized form of q deformed Sinh-Gordon equation. The underlying equation has recently undergone substantial amount of research. In Phase 1, we employed modified auxiliary and new direct extended algebraic methods. Trigonometric, hyperbolic, exponential and rational solutions are successfully extracted using these techniques, coupled with the best possible constraint requirements implemented on parameters to ensure the existence of solutions. The findings, then, are represented by 2D, 3D and contour plots to highlight the various solitons’ propagation patterns such as kink-bright, bright, dark, bright-dark, kink, and kink-peakon solitons and solitary wave solutions. It is worth emphasizing that kink dark, dark peakon, dark and dark bright solitons have not been found earlier in literature. In phase 2, the underlying model is examined under various chaos detecting tools for example lyapunov exponents, multistability and time series analysis and bifurcation diagram. Chaotic behavior is investigated using various initial condition and novel results are obtained.

Bright and dark envelope optical solitons for a (2+1)-dimensional cubic nonlinear Schrödinger equation

Purpose The purpose of this study is to investigate the nonlinear Schrödinger equation (NLS) incorporating spatiotemporal dispersion and other dispersive effects. The goal is to derive various soliton solutions, including bright, dark, singular, periodic and exponential solitons, to enhance the understanding of soliton propagation dynamics in nonlinear metamaterials (MMs) and contribute new findings to the field of nonlinear optics. Design/methodology/approach The research uses a range of powerful mathematical approaches to solve the NLS. The proposed methodologies are applied systematically to derive a variety of optical soliton solutions, each demonstrating unique optical behaviors and characteristics. The approach ensures that both the theoretical framework and practical implications of the solutions are thoroughly explored. Findings The study successfully derives several types of soliton solutions using the aforementioned mathematical approaches. Key findings include bright optical envelope solitons, dark optical envelope solitons, periodic solutions, singular solutions and exponential solutions. These results offer new insights into the behavior of ultrashort solitons in nonlinear MMs, potentially aiding further research and applications in nonlinear wave studies. Originality/value This study makes an original contribution to nonlinear optics by deriving new soliton solutions for the NLS with spatiotemporal dispersion. The diversity of solutions, including bright, dark, periodic, singular and exponential solitons, adds substantial value to the existing body of knowledge. The use of distinct and reliable methodologies to obtain these solutions underscores the novelty and potential applications of the research in advancing optical technologies. The originality lies in the novel approaches used to obtain these diverse soliton solutions and their potential impact on the study and application of nonlinear waves in MMs.

This paper explores a specific class of equations that model the propagation of optical pulses in dual-core optical fibers. The decoupled nonlinear Schrödinger equation with properties of M fractional derivatives is considered as the governing equation. The proposed model consists of group-velocity mismatch and dispersion, nonlinear refractive index and linear coupling coefficient. Different types of solutions, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted by using the integration methods known as fractional modified Sardar subequation method and modified F-expansion method. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. A fractional complex transformation is applied to reduce the governing model into the ordinary differential equation and then by the assistance of balance principle the methods are used, depending upon the balance number. Also, we plot the different graphs with the associated parameter values to visualize the solutions behaviours with different parameter values. The findings of this work will help to identify and clarify some novel soliton solutions and it is expected that the solutions obtained will play a vital role in the fields of physics and engineering.

The extended complex Ginzburg-Landau equation serves as a fundamental model for nonlinear wave dynamics, governing diverse physical phenomena ranging from particle motion in plasmas to pulse propagation in optical fibers. In this study, we introduce a hybrid analytical-machine learning framework that synergizes traditional mathematical techniques with modern data-driven approaches to comprehensively explore soliton dynamics within this system. First, we employ two advanced analytical methods, the modified Riccati extended simple equation methodology and the new modified generalized exponential rational function approach to derive a rich spectrum of nonlinear wave solutions. These include bright, dark, kink, and combined solitons, alongside hyperbolic, periodic, and exponential function solutions, thereby providing a comprehensive analytical foundation. On these analytical insights we construct a hybrid symbolic-numeric model, implemented by a multilayer perceptron regressor neural network, to find and synthesize soliton solutions to data. The key soliton types such as dark and bright solitons, combined solitons, and periodic solitons are well represented by the proposed framework with high levels of concurrence with the analytical benchmarks as seen by the low error measures. This combination provides a common platform that allows connecting classical analysis methods with modern machine learning, allowing creating as well as effectively simulating nonlinear wave behavior. This work paves the way to the frontiers of the physics of higher dimensional nonlinear waves by demonstrating the utility of this hybrid approach and highlighting some fundamental nonlinear dynamical properties of the model under consideration, and provides a paradigm that can be extended to understand the phenomena involving complex waves in interdisciplinary contexts.

The coherent manipulation and control of bright and dark solitons through sodium atomic medium have been investigated in this manuscript. Dark soliton is reported for reflection and bright soliton is reported for transmission pulses with variation in position and driving field parameters through sodium atomic medium. Further the transmission pulse is periodic dark and bright solitonic behaviors and reflection pulse is periodic bright solitonic behavior with variation in the incident angle and Rabi frequency of the control field. Elliptical dark and bright solitons as well as breather types solitons are also investigated for reflection and transmission pulses. The dark soliton in reflection is due to slow light propagation and bright soliton is obtained due to fast light propagation of transmission through the medium. The modified results of the dark and bright solitons are useful for telecommunication and ultra-fast signal routing system.

Structures solitons in birefringent fibers with Kerr and non-local laws of refractive index using improved modified extended tanh-function method

In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave and a long-wave in fluid dynamics, plasma physics and nonlinear optics, is considered. Using the Hirota bilinear method, the general N-bright and N-dark soliton solutions are deduced and their Gram determinant forms are obtained. A special feature of the fundamental bright soliton solution is that, in general, it behaves like the Korteweg-deVries soliton. However, under a special condition, it also behaves akin to the nonlinear Schrödinger soliton when it loses the amplitude-dependent velocity property. The fundamental dark-soliton solution admits anti-dark, gray, and completely black soliton profiles, in the short-wave component, depending on the choice of wave parameters. On the other hand, a bright soliton-like profile always occurs in the long-wave component. The asymptotic analysis shows that both the bright and dark solitons undergo an elastic collision with a finite phase shift. In addition to these, by tuning the phase shift regime, we point out the existence of resonance interactions among the bright solitons. Furthermore, under a special velocity resonance condition, we bring out the various types of bright and dark soliton bound states. Also, by fixing the phase factor and the system parameter \(\beta \), corresponding to the interaction between long and short wave components, the different types of profiles associated with the obtained breather solution are demonstrated.

The multiplicative white noise in the Ito interpretation is included for the first time in the perturbed higher-order modified Gerdjikov–Ivanov (HMGI) equation, that is considered the focus of the current study. In this work, we investigate the suggested model using the improved modified extended tanh-function (IMETF) method with the goal of producing brilliant and unique solitons such as dark and bright solitons, singular and singular periodic solutions, hyperbolic wave solutions, Weierstrass elliptic doubly periodic solutions, rational, exponential function solutions and Jacobi elliptic functions (JEFs). These extracted solutions demonstrate the effectiveness and potency of the used methodology. The used method specifies our research objective, which is related to solitons. These obtained soliton solutions are useful resources for examining a range of phenomena when there is white noise present. We examine how various wave phenomena are affected by noise, with a special emphasis on soliton solutions. Our findings indicate that the phase component for the obtained solitons of the suggested governing model is the primary goal of the white noise. This study is the first to show the optical soliton solutions derived from the perturbed HMGI equation under multiplicative white noise influence. The contribution of our work is the application of this phenomenon to a model equation in a new context that neither has been studied nor discovered before for optical soliton solutions. With the derived findings, our knowledge of wave events in nonlinear optical systems has advanced significantly.

This article focuses on the generalized improved Boussinesq (GIBE) equation. The GIBE equation is used to model nonlinear phenomena in various physical contexts such as shallow water waves and quantum fluid dynamics. The new extended direct algebraic method (NEDAM) is employed to obtain exact solutions to this nonlinear evolution equation. Using this method,we derive kink, anti-kink, soliton, and solitary wave solutions, including various bright, dark, and mixed-form solitons. Families of exponential, hyperbolic, and periodic wave solutions with arbitrary parameters are also obtained. The analytical solutions are visualized through explicit expressions and graphical illustrations, providing insights into wave dynamics. The findings have potential applications in optical fibers, fluid dynamics, and other engineering and physical scienceareas.

This article discusses the (2 + 1)-dimensional Hirota-Maccari (HM) model, a particular type of Schrödinger equation that addresses various nonlinear phenomena in physics, optics, fluid dynamics, plasma physics, and other scientific areas. It uses a variable relation to transform the system into an ordinary form and builds different soliton solutions using the left( {frac{{G^{prime } }}{{G^{2} }}} right)-expansion and generalized left( {frac{{G^{prime } }}{G}} right)-expansion approaches. We create double periodic waves, dark solitons, bright solitons, anti-compacton solitons, bright dark breather waves, periodic multiple waves, multiple dark-bright breather waves, compactons, and W-shaped periodic waves using the above methods plus a soft computing package. We numerically simulate some results in 3D with density, 2D, and contour formats. Additionally, we converted the dynamic planner structure of the governing model using the Galilean transformation. We then studied the chaotic properties of this model using various chaos-detecting tools, including fractal dimensions, basins of attraction, recurrence maps, strange attractors, multistability, and return maps. The significance of this study lies in its ability to bridge the theoretical understanding of the governing model with potential applications in diverse nonlinear physical systems. To our knowledge, these two methods have not yet yielded any solutions to the underlying model.

In this paper, under the observation of extended modified rational expansion method based on symbolic computation, the multiple solitary wave solutions for nonlinear two-dimensional Jaulent–Miodek Hierarchy (JMH) equation are constructed. In this investigation, we use the computer software Mathematica for the construction of multiple solitary wave solutions. The interested and important things in this work are the multiple solitary wave solutions which have various kinds of physical structures such as kink soliton, periodic traveling wave, bright soliton, anti-kink soliton, dark soliton, combined bright and dark solitons, topological soliton and peakon soliton. We are sure that the various kinds of soliton solutions are found first time by using one method in the existing literature works. On the basis of this research, we can say that the applied technique is very efficient, reliable, fruitful and powerful. The constructed soliton solutions for nonlinear JMH equation will play an important role in the investigation of different physical phenomena in nonlinear sciences.

This research explores the analytical soliton solutions of the dimensionless time-dependent paraxial equation (DTPE). We applied the improved Sardar sub-equation and improved Riccati equation analytical techniques to develop numerous soliton solutions for the DTPE, providing insights into the behavior of optical solitons in nonlinear evolution equations. The two techniques are applied for the first time to generate vigorous solutions to the DTPE. Numerous types of exponential, trigonometric, hyperbolic, dark, periodic, anti-kink, peakon, kink, and bright soliton solutions are obtained for DTPE. Although constructing an effective scheme to solve the DTPE has been our primary aim. Moreover, the obtained analytical solutions offer a useful foundation for comprehending the complex dynamics of optical solitons in nonlinear evolution equations, enabling enhancements in different applications that include signal processing, optical communication, beam shaping, Gaussian beams, lenses and mirrors, optical fibers, and predicting beam behaviors.