Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Abstract

The inspection of wave motion and propagation of diffusion, convection, dispersion, and dissipation is a key research area in mathematics, physics, engineering, and real-time application fields. This article addresses the generalized dimensional Hirota–Maccari equation by using two different methods: the exp(−φ(ζ)) expansion method and Addendum to Kudryashov’s method to obtain the optical traveling wave solutions. By utilizing suitable transformations, the nonlinear pdes are transformed into odes. The traveling wave solutions are expressed in terms of rational functions. For certain parameter values, the obtained optical solutions are described graphically with the aid of Maple 15 software.

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

“…Let us look for the solution of Equation ( 12) using the logistic function. We assume that there exist a solution of Equation ( 12) in the form [37][38][39][40][41][42][43][44][45][46]…”

Investigation of optical soliton solutions for the perturbed Gerdjikov-Ivanov equation with full-nonlinearity

“…In this article, we investigate the pGI equation by two efficient analytical techniques. Sardar subequation method (SSM) [24] , [60] and modified new Kudryashov method (mNKM) [61] , [62] . Organization of the paper as follows; in section 2 , obtaining nonlinear ordinary differential equation (NODE), implementation of the methods is included.…”

Explore Optical Solitary Wave Solutions of the kp Equation by Recent Approaches

“…Over the past few years, numerous strategies have been proposed by mathematicians and scientists, such as the F-expansion method [8], the variational iteration method [9], method of sine-cosine [10], the tanh-function technique [11], the auxiliary equation method [12], the exp-function technique [13,14], the exact soliton solution [15][16][17], the generalized Kudryashov approach [18], and the newly extended generalized Kudryashov approach [19]. A more detailed discussion on some recent direct methods can be found in several related works (see, for example, [20][21][22][23]).…”