VARIATIONAL APPROACHES TO CONSERVATION LAWS FOR A NONLINEAR EVOLUTION EQUATION WITH TIME DEPENDENT COEFFICIENTS

被引：5

作者：

Johnpillai, A. G. ^{[1
]}

Khalique, C. M. ^{[1
]}

机构：

[1] North West Univ, Int Inst Symmetry Anal & Math Modelling, Dept Math Sci, ZA-2735 Mmabatho, South Africa

来源：

QUAESTIONES MATHEMATICAE | 2011年 / 34卷 / 02期

关键词：

Modified KdV equation; Lie point symmetries; adjoint equation; partial Lagrangian; partial Noether operators; conservation laws; PARTIAL-DIFFERENTIAL-EQUATIONS; DIRECT CONSTRUCTION METHOD; SYMMETRIES;

D O I：

10.2989/16073606.2011.594238

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The conservation laws of a nonlinear evolution equation of time dependent variable coefficients of damping and dispersion is studied. The equation under consideration is not derivable from a variational principle which means that one cannot appeal to the Noether theorem to determine the conservation laws. We utilize the new conservation theorem (N.H. Ibragimov, [8]) and the partial Lagrangian approach (A.H. Kara, F.M. Mahomed, [13]) to construct local, and infinite number of nonlocal conservation laws (due to the transformation of the dependent variable) of the underlying equation.

引用

页码：235 / 245

页数：11

共 23 条

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