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In this article, the sine-Gordon expansion method is employed to find some new traveling wave solutions to the nonlinear Schrödinger equation with the coefficients of both group velocity dispersion and second-order spatiotemporal dispersion. The nonlinear model is reduced to an ordinary differential equation by introducing an intelligible wave transformation. A set of new exact solutions are observed corresponding to various parameters. These novel soliton solutions are depicted in figures, revealing the new physical behavior of the acquired solutions. The method proves its ability to provide good new approximate solutions with some applications in science. Moreover, the associated solution of the presented method can be extended to solve more complex models.

The purpose of this article is to construct some novel exact travelling and solitary wave solutions of the time fractional (2 + 1) dimensional Konopelchenko–Dubrovsky equation, and two different forms of integration schemes have been utilized in this context. As a result, a variety of bright and dark solitons, kink- and antikink-type solitons, hyperbolic functions, trigonometric functions, elliptic functions, periodic solitary wave solutions and travelling wave solutions are obtained, and the sufficient conditions for the existence of solution are also discussed. Moreover, some of the obtained solutions are illustrated as two- and three-dimensional graphical images by using computational software Mathematica. These types of solutions have a wide range of applications in applied sciences and mathematical physics. The proposed methods are very useful for solving nonlinear partial differential equations arising in physical science and engineering.

This paper investigates the analytical solutions of the perturbed nonlinear Schrödinger equation through the modified Khater method. This method is considered one of the most recent accurate analytical schemes in nonlinear evolution equations where it obtained many distinct forms of solutions of the considered model. The investigated model in this paper is an icon in quantum fields where it describes the wave function or state function of a quantum-mechanical system. The physical characterization of some obtained solutions in our study is explained through sketching them in two- and three-dimensional contour plots. The novelty of our study is clear by showing the matching between our solutions and those that have been constructed in previously published papers. [ABSTRACT FROM AUTHOR]

In this paper, the auxiliary equation method is successfully applied to compute analytical solutions for (3+1)-dimensional generalised Kadomtsev-Petviashvili and (2+1)-dimensional Gardner-Kadomtsev-Petviashvili equations, by introducing simple transformations. These results hold numerous travelling wave solutions that are of key importance which provide a powerful mathematical tool for solving nonlinear wave equations in recent era of applied science and engineering. The method can also be extended to other nonlinear evolution models arising in contemporary physics. [ABSTRACT FROM AUTHOR]