A Maple package for verifying ultradiscrete soliton solutions

Gao Min

Ito Masaaki

Computer Physics Conmunications

We present a Computer algebra program for verifying soliton solutions of ultradiscrete equations in which both dependent and independent variables take discrete values. The package is applicable to equations and solutions that include the max function. The program is implemented using Maple software. Program summary Program title: Ultde Catalogue identifier: AEDB_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3171 No. of bytes in distributed program, including test data, etc.: 13633 Distribution format: tar.gz Programming language: Maple 10 Computer: PC/AT compatible machine Operating system: Windows 2000, Windows XP RAM: Depends on the problem: minimum about 1 GB Wordsize: 32 bits Classification: 5 Nature of problem: The existence of multi-soliton solutions strongly suggest the integrability of nonlinear evolution equations. However enormous calculation is required to verify multi-soliton solutions of ultradiscrete equations. The use of computer algebra can be helpful in such calculations. Solution method: Simplification by using the properties of max-plus algebra. Restrictions: The program can only handle single ultradiscrete equations. Running time: Depends on the complexity of the equation and solution. For the examples included in the distribution the run times are as follows. (Core 2 Duo 3 GHz, Windows XP) Example 1: 2725 sec. Example 2: 33 sec. Example 3: 1 sec

Ultradiscrete equations

Soliton solutions

Max-plus algebra

Computer algebra

Electrical engineering [ 540 ]

eng

Elsevier Science Bv

Copyright (c) 2009 Elsevier B.V.

[ISSN] 0010-4655

[DOI] 10.1016/j.cpc.2009.01.009

[NCID] AA00613344

[DOI] http://dx.doi.org/10.1016/j.cpc.2009.01.009