Abstract
We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein‐Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jacobi elliptic solutions are obtained for some nonlinear differential difference equations in mathematical physics. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.
Highlights
In recent years, the study of difference equations has acquired a new significance, due in large part to their use in the formulation and analysis of discrete-time systems, the numerical integration of differential equation by finite-difference schemes and the study of deterministic chaos.Since the work of Fermi et al in the 1960s 1, DDEs have been the focus of many nonlinear studies
A considerable number of well-known analytic methods are successfully extended to nonlinear DDEs by researchers 2–17
Further using the properties of Jacobi elliptic functions, the iterative relations can be written in the following form: U ξn±p
Summary
The study of difference equations has acquired a new significance, due in large part to their use in the formulation and analysis of discrete-time systems, the numerical integration of differential equation by finite-difference schemes and the study of deterministic chaos. Shehata 22 have used the Jacobi elliptic function method for constructing new and more general Jacobi elliptic function solutions of the nonlinear differential difference equations. The main objective of this paper is to modify the rational Jacobi elliptic functions method to obtain the exact wave solutions for nonlinear DDEs. The main objective of this paper is to modify the rational Jacobi elliptic functions method to obtain the exact wave solutions for nonlinear DDEs We use this method to calculate the exact wave solutions for some nonlinear DDEs in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation
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