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This paper introduces a novel model proposed by Wazwaz et al. in 2023, in the nonlinear optics literature. This contributes to advancing optical devices and technologies, particularly in telecommunications and laser systems. The characteristics of bright, dark, and periodic soliton solutions for the (2+1)-dimensional nonlinear Schrödinger equation with fourth-order nonlinearity and dispersion are explored in this paper. The relevance of these solutions lies in the study of nonlinear waves propagating in an inhomogeneous optical fiber. The soliton solutions are obtained through the implementation of three analytical methods: the Kudryashov method, the Bernoulli Sub-ODE method, and the Extended Direct Algebraic method. The bright, dark, and periodic soliton solutions are constructed by utilizing bilinear forms. Furthermore, the impact of variable coefficients on the structures of these solitons is analyzed. Graphical illustrations depict the propagation of bright, dark, and periodic solitons. [ABSTRACT FROM AUTHOR]

The main goal of the article is to present the optical soliton solutions of the nonlinear Schrodinger equation, comprising Kudryashov's quintuple power-law with dual form nonlinearity which has very important applications in domination soliton pulse propagation through optical fibers and photonic crystal fibers. To achieve our goal, two potent analytical techniques are employed: the Sardar-Subequation method and the new method G ′ k G ′ + G + r -expansion method, which represent a novel approach not found in existing literature. Furthermore, our approach offers distinctive solutions characterized by a rich variety of trigonometric and hyperbolic functions. The majority of our results are depicted graphically to highlight our achievements. [ABSTRACT FROM AUTHOR]

In this work, we investigate the solutions of the (2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation by three powerful analytical methods: the exp a function method, the (G ′ G) -expansion method, and the Sine-Gordon expansion method. This equation describes the nonlinear wave propagation in many applications like waves of evolutionary shallow water, electrical networks, and engineering devices. Moreover, we study the solutions numerically via the finite difference method. We analyze the bifurcation of dynamical system resulting from the BKP equation. Finally, the majority of our solutions are displayed graphically to present the strength of imposed methods. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation's natural protraction, the (2+1) Fokas system, illustrates how a pulse moves across monomode optical fibers. Three efficient methods the Sardar sub-equation approach, the Bernoulli sub-ODE method, and the generic Kudryashov's method are used in this study to offer various families of solutions. Several sorts of function solutions, including those for hyperbolic, trigonometric, power, exponential, and rational functions, are provided by our suggested approaches. In order to highlight the many solutions found, numerous graphs are given toward the conclusion of the text. [ABSTRACT FROM AUTHOR]

In this paper, we present the analytic and numerical solutions of the newly modified Zakharov–Kuznetsov equation. This model is used to study the waves in different plasmas. The analytical solutions were achieved by the extended tanh method and the Sine Gordon method while the numerical one is achieved by the implicit finite difference method and the local truncation error and the stability analysis for the difference scheme are given. Graphical representations of exact and numerical solutions are given to illustrate our results. In addition to the other known results in the literature, the paper contributes new analytical and numerical results. [ABSTRACT FROM AUTHOR]