A Maple package for finding exact solitary wave solutions of coupled nonlinear evolution equations

Abstract The tanh function expansion method for finding traveling solitary wave solutions to coupled nonlinear evolution equations is described. A complete implementation RATHS written in Maple is presented, in which the operator mains can output exact solitary wave solutions entirely automatically. Furthermore, RATHS can handle any number of dependent variables u i as well as any number of independent variables x j contained in the input system. This package can also be applied to ODEs. The effectiveness of RATHS is illustrated by applying it to a variety of equations. Program summary Title of program: RATHS Catalogue identifier: ADSD (also ADQK) Program Summary URL: http://cpc.cs.qub.ac.uk/summaries/ADRY (also ADQR) Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers: PC Pentium IV Installations: Copy Operating systems: Windows 98/2000/XP Program language used: Maple V R6 Memory required to execute with typical data: depends on the problem, minimum about 8M words No. of bits in a word: 8 No. of bytes in distributed program, including the test data, etc.: 16 608 Distribution format: tar gzip file Keywords: Coupled nonlinear evolution equations, traveling solitary wave solutions, dependent variable, independent variable Nature of physical problem: Our program give out exact solitary wave solutions, which can describe various phenomena in nature, and thus can give more insight into the physical aspects of problems and may be easily used in further applications. Restriction on the complexity of the problem: The program can handle coupled nonlinear evolution equations, in which every equation is a polynomial (or can be converted to a polynomial) in the unknown functions and their derivatives. Typical running time: It depends on the input equations as well as the degrees of the desired polynomial solutions. For most of the coupled equations which we have computed, the running time is no more than 20 seconds.

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