Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Abstract

We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations

“…They also play an important role in numerical simulation of solution dynamics in high-energy physics because of their rich structures. Therefore, researchers have shown a wide interest in studying NDDEs since the original work of Fermi et al [1] in the 1950s and [2,3]. Contrary to difference equations that are being fully discretized, NDDEs are semidiscretized, with some (or all) of their space variables being discretized, while time is usually kept continuous.…”

“…The objective of the present paper is to extend the application of the HPTM to obtain an analytic approximate solution of the following nonlinear difference differential equations in mathematical physics: (i) the general lattice equation [1][2][3]:…”