Application of Tanh Method to Complex Coupled Nonlinear Evolution Equations

Abstract

This paper studies the application of tanh method to address a few coupled nonlinear evolution equations that are in complex domain. There are soliton solutions as well as triangular solutions that are revealed with this integration scheme. The equations studied in this paper are applicable to various branches of applied and theoretical physics.

Three kinds of periodic wave solutions and their limit forms for a modified KdV-type equation

“…From (50), (51) and (2), we obtain the periodic blow-up wave solutions as (17). Substituting (46) and (47) into the dφ dξ = y and integrating them along the open curves, respectively, we have…”

“…Many powerful methods have been presented for finding the traveling wave solutions of nonlinear partial differential equations, such as the Bäcklund transformation [10], Darboux transformation [11], inverse scattering method [12], Hirota bilinear method [13], Lie group analysis method [14][15][16], tanh method [17], ansatz method [18,19], bifurcation theory of dynamical system [20,21], exp-function method [22,23], symbolic computation method [24][25][26], and other methods [27][28][29][30].…”

Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers

“…Let us consider Case 1 and use the tanh method. To the best of our knowledge paper [15] is one of the earliest works devoted to the tanh method (there are a lot recent papers, see, e.g., [17,27] and papers cited therein). However, it can be noted that there are not many papers devoted to application of this method to nonlinear systems of PDEs.…”

Analytical study of solitons in non-Kerr nonlinear negative-index materials

“…(1), we use the following wave transformation [11][12][13][14][15][16] q(x, t) = U (ξ )e i (x,t) (2) where U (ξ ) represents the shape of the pulse and…”