A comparison of four approaches to the calculation of conservation laws

被引：117

作者：

Wolf, T ^{[1
]}

机构：

[1] Brock Univ, Dept Math, St Catharines, ON L2S 3A1, Canada

来源：

EUROPEAN JOURNAL OF APPLIED MATHEMATICS | 2002年 / 13卷

关键词：

D O I：

10.1017/S0956792501004715

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper compares computational aspects of four approaches to compute conservation laws of single Differential Equations (DEs) or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer algebra programs, is that each DE has to be solvable for a leading derivative. Extra constraints for the conservation laws can be specified. Examples include new conservation laws that are non-polynomial in the functions, that have an explicit variable dependence and families of conservation laws involving arbitrary functions. The following equations are investigated in examples: Ito, Liouville, Burgers, Kadomtsev-Petviashvili, Karney-Sen-Chu-Verheest, Boussinesq, Tzetzeica, Benney.

引用

页码：129 / 152

页数：24

共 35 条

[21] LeVeque R. J., 1992, Numerical Methods for Conservation Laws, V2nd ed., DOI DOI 10.1007/978-3-0348-8629-1
[22] Mikhailov A. V., 1979, PISMA ESKP TEOR FIZ, V30, P443
[23] EXTENSION OF THE MODULE OF INVERTIBLE TRANSFORMATIONS - CLASSIFICATION OF INTEGRABLE SYSTEMS
MIKHAILOV, AV
SHABAT, AB
YAMILOV, RI
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 115 (01) : 1 - 19
[24] MIKHAILOV AV, 1987, SOV MATH DOKL, V295, P288
[25] THE HISTORY OF THE SOLITON
NEWELL, AC
[J]. JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1983, 50 (4B): : 1127 - 1138
[26] CONSERVATION-LAWS AND NULL DIVERGENCES
OLVER, PJ
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1983, 94 (NOV) : 529 - 540
[27] Olver PJ., 1986, Applications of Lie groups to differential equations
[28] BACKLUND TRANSFORMATION FOR A HIGHER-ORDER KORTEWEG-DEVRIES EQUATION
SATSUMA, J
KAUP, DJ
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1977, 43 (02) : 692 - 697
[29] METHOD FOR FINDING N-SOLITON SOLUTIONS OF KDV EQUATION AND KDV LIKE EQUATION
SAWADA, K
KOTERA, T
[J]. PROGRESS OF THEORETICAL PHYSICS, 1974, 51 (05): : 1355 - 1367
[30] SHABAT A, 1979, DOKLADY ACAD NAUK SS, V247

← 1 2 3 4 →