CONSLAW: A Maple package to construct the conservation laws for nonlinear evolution equations

摘要

An improved algorithm to explicitly compute the polynomial-type conservation laws for nonlinear evolution equations (either uniform in rank or not) is introduced and a software package CONSLAW written in Maple to automate the computation is developed. CONSLAW can construct the polynomial-type conservation laws for polynomial partial differential equations automatically. Furthermore, some new integrable systems can be filtered out by analyzing the compatibility conditions, which guarantee the existence of the conservation laws for a given parameterized nonlinear evolution equations. The explicit forms of the conserved densities play an important role in studying the integrability, such as explicit analytical solutions, bi-Hamiltonian form, one-parameter family of Bäcklund transformations, Lax pairs, and the checking of the accuracy of numerical integration algorithm. The effectiveness of CONSLAW is illustrated by applying it to a variety of equations.