Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions

被引：26

作者：

Poole, Douglas ^{[1
]}

Hereman, Willy ^{[2
]}

机构：

[1] Chadron State Coll, Dept Math Sci, Chadron, NE 69377 USA

[2] Colorado Sch Mines, Dept Appl Math & Stat, Golden, CO 80401 USA

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2011年 / 46卷 / 12期

基金：

美国国家科学基金会;

关键词：

Conservation laws; Nonlinear PDEs; Symbolic software; Complete integrability; SYMMETRIES; EVOLUTION; OPERATORS; WAVES;

D O I：

10.1016/j.jsc.2011.08.014

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A method for symbolically computing conservation laws of nonlinear partial differential equations(PDEs) in multiple space dimensions is presented in the language of variational calculus and linear algebra. The steps of the method are illustrated using the Zakharov-Kuznetsov and Kadomtsev-Petviashvili equations as examples. The method is algorithmic and has been implemented in Mathernatica. The software package, CONSERVATIONLAWSMD.M, can be used to symbolically compute and test conservation laws for polynomial PDEs that can be written as nonlinear evolution equations. The code CONSERVATIONLAWSMD.M has been applied to multidimensional versions of the Sawada-Kotera, Camassa-Holm, Gardner, and Khokhlov-Zabolotskaya equations. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1355 / 1377

页数：23

共 44 条

[1]

Ablowitz M.J., 1991, Nonlinear Evolution Equations and Inverse Scattering

[2]

Ablowitz M. J., 1981, SIAM STUD APPL MATH, V4

[3]

ANDERSON IM, 2004, VARIATIONAL CO UNPUB

[4]

ANDERSON IM, 2009, DIFFERENTIALGEOMETRY

[5]

ANDERSON IM, 2004, VESSIOT PACKAGE

[6]

[Anonymous], 1993, GRAD TEXTS MATH

[7] A symbolic algorithm for computing recursion operators of nonlinear partial differential equations [J].

Baldwin, D. E. ;

Hereman, W. .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (05) :1094-1119

[8]

Bluman G. W., 2010, APPL MATH SCI, V168

[9] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664

[10]

CHEBTERRAB E, 2004, PDETOOLS PACKAGE MAP

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