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One of the most important physical models for describing the dynamics of optical soliton propagation in the theory of optical fibers is the nonlinear Schrödinger equation (NLSE). Since there are so many uses for ultrafast signal routing systems and brief light pulses in telecommunication, optical soliton propagation in nonlinear optical fibers is a subject of intense current interest. The conventional Khater approach and the extended direct algebraic method are used in this research to study a generalized unstable space–time fractional NLS model in mathematical physics. This leads to the discovery of solutions for the bright, dark, periodic, rational and elliptic functions. To illustrate the physical nature of the nonlinear model, the contour plots in 3D, 2D and 2D are produced by assigning the appropriate values to the arbitrary constants. Additionally, consideration is given to the stability analysis of the solutions to the governing equation. In the current era of communications network technology and nonlinear optics, the applied strategy appears to be a more potent and effective way for producing precise optical solutions to a number of various modern models of recent generations. [ABSTRACT FROM AUTHOR]

The Allen–Cahn equation (ACE), which has applications in solid-state physics, imaging, plasma physics, material science and other fields, is one of the most important models of the modern era for describing the dynamics of oil pollution, reaction-diffusion mechanisms, and the mechanics of crystalline solids. By using the (1 G ′ ) -expansion method (GEM) and the Bernoulli sub-ODE schemes, some new traveling wave solutions for the governing model are created in this study (BSODE). The reduced integrable ordinary differential equation is produced using the traveling wave hypothesis. To better understand their behavior, the 3D, contour, and 2D graphs are displayed for a number of fascinating exact solutions. Additionally, we use numerical simulation to confirm the stability of the derived analytical solutions. It results the propagation of temporal soliton for long time of simulation. These results will be used to explain physical phenomenon in crystalline solids and others fields. [ABSTRACT FROM AUTHOR]

In this paper, we study the perturbed nonlinear Schrödinger equation (P-NLSE) representing the propagation of waves and may be regarded as a nonlinear complicated physical model. We use the modified extended Tan hyperbolic function (METhF) approach and the ( G ′ G 2 ) -expansion approach to construct some new traveling wave structures. Several solutions have been found including dark soliton, periodic-type solitons, bell-shaped solitons, single bell-shaped solitons. We also show a graphical representation of a number of exact solutions to the dynamical model together with a description of their behavior. The proposed techniques can also be extended to various nonlinear evolution models in mathematical physics and engineering. [ABSTRACT FROM AUTHOR]

In this paper, the auxiliary expansion equation method is applied to compute the analytical wave solutions for (3 + 1)-dimensional Boussinesq and Kadomtsev–Petviashvili (KP) equations. A simple transformation is carried out to reduce the set of nonlinear partial differential equations (NPDEs) into ODEs. These obtained results hold numerous traveling wave solutions that are of key importance in elucidating some physical circumstance. [ABSTRACT FROM AUTHOR]