Symbolic computation of hyperbolic tangent solutions for nonlinear differential–difference equations

Abstract
A new algorithm is presented to find exact traveling wave solutions of differential–difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the equations might admit polynomial solutions in tanh. Examples illustrate the key steps of the algorithm. Through discussion and example, parallels are drawn to the tanh-method for partial differential equations. The new algorithm is implemented in Mathematica. The p...

Title of program: DDESpecialSolutions.m
Catalogue Id: ADUJ_v1_0

Nature of problem
The program computes exact solutions to differential-difference equations in terms of the tanh function. Such solutions describe particle vibrations in lattices, currents in electrical networks, pulses in biological chains, etc.

Versions of this program held in the CPC repository in Mendeley Data
ADUJ_v1_0; DDESpecialSolutions.m; 10.1016/j.cpc.2004.07.002

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要
本文提出一种新算法，用于求解以双曲正切（tanh）函数表示的微分-差分方程（differential–difference equations）的精确行波解（exact traveling wave solutions）。针对含参数的系统，该算法可确定参数需满足的约束条件，使得方程可获得关于tanh的多项式解。算例阐明了该算法的核心步骤。通过讨论与实例，本文还将该新算法与偏微分方程的tanh方法进行了类比。该新算法已在Mathematica中实现。[原文此处存在截断]

程序名称：DDESpecialSolutions.m
目录编号：ADUJ_v1_0

问题本质
本程序用于求解以双曲正切（tanh）函数形式表示的微分-差分方程精确解。此类解可用于描述晶格中的粒子振动、电路中的电流、生物链中的脉冲等诸多场景。

本程序在Mendeley数据的CPC资源库中的留存版本为：ADUJ_v1_0；DDESpecialSolutions.m；10.1016/j.cpc.2004.07.002

本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018年）