New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the (2 + 1)‐Dimensional Evolution Equation

Abstract

The generalized Riccati equation mapping is extended with the basic(G′/G)-expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1)-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equationG′(η)=w+uG(η)+vG2(η)is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple.

New approach of (G′/G)-expansion method and new approach of generalized (G′/G)-expansion method for nonlinear evolution equation

“…In the recent past, a wide range of methods have been developed to generate analytical solutions by a diverse group of scientists. For instance, the Backlund transformation method, 1 the inverse scattering method, 2 the truncated Painleve expansion method, 3 the Weirstrass elliptic function method, 4 the Hirota's bilinear transformation method, 5 the Jacobi elliptic function expansion method, 6 the generalized Riccati equation method, 7,8 the tanh-coth method, 9, 10 the F-expansion method, 11,12 the variational iteration method, 13 the direct algebraic method, 14 the homotopy perturbation method, 15,16 the Exp-function method 17,21 and others. 22,27 Another important method was introduced by Wang et al 28 to obtain exact solutions of some nonlinear partial differential equations (PDEs), which is called the (G /G)-expansion method.…”

New Exact Solutions of Ion-Acoustic Wave Equations by (G′/G)-Expansion Method

“…In fact, the ( / )-expansion method has been successfully applied to obtain exact solution for a variety of NLPDE [23][24][25][26][27][28][29][30][31][32][33][34].…”

Peaked and Smooth Solitons forK*(4,1)Equation

“…In the development of soliton theory, there exist many different approaches to searching for exact solutions of nonlinear partial differential equations, such as mapping method [6], fan-expansion method [7], and ( / )expansion method [8]. In particular, it is very interesting to investigate the traveling wave solutions on a constant pedestal.…”