ON THE REDEFINITION OF THE VARIATIONAL AND 'PARTIAL' VARIATIONAL CONSERVATION LAWS IN A CLASS OF NONLINEAR PDEs WITH MIXED DERIVATIVES

被引：10

作者：

Narain, R. ^{[1
]}

Kara, A. H. ^{[1
]}

机构：

[1] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, Johannesburg, South Africa

来源：

MATHEMATICAL AND COMPUTATIONAL APPLICATIONS | 2010年 / 15卷 / 04期

关键词：

Noether's theorem; mixed derivatives; conservation laws; SYMMETRIES;

D O I：

10.3390/mca15040732

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The construction of conserved vectors using Noether's and partial Noether's theorems are carried out for high order PDEs with mixed derivatives. The resultant conserved flows display some interesting 'divergence properties' owing to the existence of the mixed derivatives. These are spelled out for various equations from mathematical physics.

引用

页码：732 / 741

页数：10

共 10 条

[1]

ANCO S, 2009, SYMMETRY INVARIANCE

[2] Direct construction method for conservation laws of partial differential equations - Part I: Examples of conservation law classifications [J].

Anco, SC ;

Bluman, G .

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2002, 13 :545-566

[3]

[Anonymous], 1918, NACHR GES WISS GOETT

[4] On the inverse scattering approach to the Camassa-Holm equation [J].

Constantin, A ;

Lenells, J .

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2003, 10 (03) :252-255

[5] Backlund transformations for many-body systems related to KdV [J].

Hone, ANW ;

Kuznetsov, VB ;

Ragnisco, O .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1999, 32 (27) :L299-L306

[6]

Ibragimov N. H., 1985, TRANSFORMATION GROUP

[7] Noether-type symmetries and conservation laws via partial Lagrangians [J].

Kara, A. H. ;

Mahomed, F. A. .

NONLINEAR DYNAMICS, 2006, 45 (3-4) :367-383

[8] Relationship between symmetries and conservation laws [J].

Kara, AH ;

Mahomed, FM .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2000, 39 (01) :23-40

[9] Weak geodesic flow and global solutions of the Hunter-Saxton equation [J].

Lenells, Jonatan .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2007, 18 (04) :643-656

[10]

NARAIN R, PHYS LETT A UNPUB

← 1 →