PDEBellII: A Maple package for finding bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type equations

Abstract

Based on the Bell polynomials scheme, this paper presents a Maple computer algebra program PDEBellII which can automatically construct the bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type soliton equations. Some examples are given to verify the validity of our program. Program summaryProgram title: PDEBellIICatalogue identifier: AEQP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQP_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2170No. of bytes in distributed program, including test data, etc.: 43827Distribution format: tar.gzProgramming language: Maple internal language.Computer: PCs, Dell OptiPlex 390.Operating system: Windows XP and Windows 7.RAM: Depends on the complexity of the problem (MB)Classification: 4.3, 5.Nature of problem:Determination of integrability of the nonlinear evolution equations, including bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws.Solution method:The package PDEBellII is developed by using the Bell polynomials which is linked with Hirota operators.Restrictions:The program can only handle single nonlinear evolution equations.Unusual features:The program PDEBellII is the first Maple automatic program to construct bilinear Bäcklund transformations, Lax pairs and the infinite conservation laws for nonlinear evolution equations.Running time:Depends strongly on the complexity of the equation. Different tasks take from 0.4 to 20 s.