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Manuscript Title: Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations
Authors: D. Baldwin, Ü. Göktas, W. Hereman
Program title: DDESpecialSolutions.m
Catalogue identifier: ADUJ
Journal reference: Comput. Phys. Commun. 162(2004)203
Programming language: Mathematica, version 3.0 or higher.
Computer: Created using a PC, but can be run on UNIX and Apple machines.
Operating system: Windows 2000 and XP.
Keywords: Exact solutions, traveling wave solutions, differential-difference equations, semi-discrete lattices, tanh-method.
PACS: 02.70.Wz, 02.30.Ik, 02.30.Jr, 02.90.+p.
Classification: 5, 4.3.

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.

Solution method:
After the differential-difference equation is put in a traveling frame of reference, the coefficients of a candidate polynomial solution in tanh are solved for. The resulting traveling wave solutions are tested by substitution into the original differential-difference equation.

The system of differential-difference equations must be polynomial. Solutions are polynomial in tanh.

Running time:
The average run time of 16 cases (including the Toda, Volterra, and Ablowitz-Ladik lattices) is 0.228 seconds with a standard deviation of 0.165 seconds on a 2.4GHz Pentium 4 with 512 MB RAM running Mathematica 4.1. The running time may vary considerably, depending on the complexity of the problem.