The discrete (G′/G)‐expansion method applied to the differential‐difference Burgers equation and the relativistic Toda lattice system

Abstract

We introduce the discrete (G /G)-expansion method for solving nonlinear differential-difference equations (NDDEs). As illustrative examples, we consider the differential-difference Burgers equation and the relativistic Toda lattice system. Discrete solitary, periodic, and rational solutions are obtained in a concise manner. The method is also applicable to other types of NDDEs.

Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

“…Zhang et al [21] have modified the ( / ) expansion method form solving the nonlinear partial differential equations to solve the nonlinear differential difference equations. Aslan [22,23] has applied the ( / ) expansion method for solving the discrete nonlinear Schrodinger equations with a saturable nonlinearity, discrete Burgers equation, and the relativistic Toda lattice system. More recently Gepreel et al [24][25][26] have used the modified rational Jacobi elliptic functions method to construct some types of Jacobi elliptic solutions of the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, and the quintic discrete nonlinear Schrodinger equation.…”

Some exact solutions for Toda type lattice differential equations using the improved (G′/G)‐expansion method

“…Naturally, the method has been extended, generalized and adapted by others [15][16][17] for various kinds of nonlinear problems. It is also remarkable that the generalization presented in [18] can be considered as a new step in studying NPDEs, see [19][20][21][22][23][24] for further applications. The present paper is a worthwhile contribution to this effort as well.…”