New Optical Solitons And Modulation Instability Analysis of Generalized Coupled Nonlinear Schrodinger-KdV System

In this study, the generalized coupled nonlinear Schrodinger-KdV (NLS-KdV) system is investigated to obtain new optical soliton solutions. This system appears as a model for reciprocity between long and short waves in various of physical settings. Different kind of new soliton solutions including dark, bright, combined dark-bright, singular and combined singular soliton solutions are obtained using two effective methods namely, the extended sinh-Gordon equation expansion method and the solitary wave ansatz method. In addition, the modulation instability analysis of the system is presented based on the standard linearstability analysis. The behaviours of obtained solutions are expressed by 3D graphs.

Highly Dispersive Optical Solitons with Complex Ginzburg–Landau Equation Having Six Nonlinear Forms

This paper retrieves highly dispersive optical solitons to complex Ginzburg–Landau equation having six forms of nonlinear refractive index structures for the very first time. The enhanced version of the Kudryashov approach is the adopted integration tool. Thus, bright and singular soliton solutions emerge from the scheme that are exhibited with their respective parameter constraints.

Highly dispersive optical soliton perturbation of Kudryashov’s arbitrary form having sextic-power law refractive index

In this research paper, a simple integration scheme is executed to secure new dark and singular soliton solutions for the highly dispersive nonlinear Schrödinger’s equation having Kudryashov’s arbitrary form with generalized nonlocal laws and sextic-power law refractive index.

Optical Solitons in Bragg Gratings Fibers for The Nonlinear (2+1)-Dimensional Kundu-Mukherjee-Naskar Equation Using Two Integration Schemes

The current work handles for the first time, dispersive optical solitons in fiber Bragg gratings for the nonlinear (2+1)-dimensional Kundu-Mukherjee-Naskar equation. Two integration schemes, namely, the modified Kudryashov's approach and the addendum to Kudryashov's methodology are applied. Dark, bright and singular soliton solutions are obtained. Also, combo bright-singular soliton solutions are introduced.

Refraction simulation of internal solitary waves for the fractional Benjamin–Ono equation in fluid dynamics

In this study, the modified [Formula: see text]-expansion method and modified sub-equation method have been successfully applied to the fractional Benjamin–Ono equation that models the internal solitary wave event in the ocean or atmosphere. With both analytical methods, dark soliton, singular soliton, mixed dark-singular soliton, trigonometric, rational, hyperbolic, complex hyperbolic, complex type traveling wave solutions have been produced. In these applications, we consider the conformable operator to which the chain rule is applied. Special values were given to the constants in the solution while drawing graphs representing the stationary wave. By making changes of these constants at certain intervals, the refraction dynamics and physical interpretations of the obtained internal solitary waves were included. These physical comments were supported by simulation with 3D, 2D and contour graphics. These two analytical methods used to obtain analytical solutions of the fractional Benjamin–Ono equation have been analyzed in detail by comparing their respective states. By using symbolic calculation, these methods have been shown to be the powerful and reliable mathematical tools for the solution of fractional nonlinear partial differential equations.

New optical soliton solutions of the Chen–Lee–Liu equation

In this work, we demonstrate the extraction of some optical soliton solutions of the Chen–Lee–Liu equation (CLLE) with applications in optical fibers. A novel method is presented which is called the new extended direct algebraic method (EDAM). This method is based on converting the nonlinear CLLE equation into an ordinary type equation through a wave transformation. We acquire new solutions like dark, bright, combined dark-bright, combined bright-singular and periodic singular soliton solutions by using this effective technique. These acquired soliton solutions are new with some new physical properties. Some graphical representations for these solutions are provided which prove that the new method is effective and can be extended to some similar problems.

Embedded solitons with χ(2) and χ(3) nonlinear susceptibilities

GStudied in this work are embedded solitons with quadratic nonlinearity that includes the effect of spatio-temporal dispersion. Two integration schemes yield bright, dark, singular and combo singular soliton solutions from the continuous regime. The existence criteria for these solitons are also included.

Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics

In this study, analytical solutions and physical interpretations are presented for the Riemann wave equation (RWE), which has an important physical property in fluid dynamics. The solutions of the RWE, which models the formation, interaction and breaking of the waves that occur as a result of any external effect on the ocean surface, are examined using the generalized exponential rational function method (GERFM). Bright (nontopological) soliton, singular soliton and solitary wave solutions are produced with advantages of GERFM over other traditional exponential methods. The factors in which solitary wave solutions cause breaking of wave are examined. The effects of parameters on wavefunctions and the physical interpretations of these effects are discussed and supported by graphics and simulations.

New and More Solitary Wave Solutions for the Klein-Gordon-Schrödinger Model Arising in Nucleon-Meson Interaction

This paper considers methods to extract exact, explicit, and new single soliton solutions related to the nonlinear Klein-Gordon-Schrödinger model that is utilized in the study of neutral scalar mesons associated with conserved scalar nucleons coupled through the Yukawa interaction. Three state of the art integration schemes, namely, the e−Φ(ξ)-expansion method, Kudryashov's method, and the tanh-coth expansion method are employed to extract bright soliton, dark soliton, periodic soliton, combo soliton, kink soliton, and singular soliton solutions. All the constructed solutions satisfy their existence criteria. It is shown that these methods are concise, straightforward, promising, and reliable mathematical tools to untangle the physical features of mathematical physics equations.