Conservation laws of KdV equation with time dependent coefficients

被引：23

作者：

Johnpillai, A. G. ^{[1
,2
]}

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

机构：

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

[2] Eastern Univ, Dept Math, Batticaloa, Sri Lanka

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2011年 / 16卷 / 08期

关键词：

Generalized KdV equation; Lie symmetries; Adjoint equations; Partial Lagrangian; Partial Noether operators; Conservation laws; PARTIAL-DIFFERENTIAL-EQUATIONS; DIRECT CONSTRUCTION METHOD; SYMMETRIES;

D O I：

10.1016/j.cnsns.2010.10.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We determine conservation laws of the generalized KdV equation of time dependent variable coefficients of the linear damping and dispersion. The underlying equation is not derivable from a variational principle and hence one cannot use Noether's theorem here to construct conservation laws as there is no Lagrangian. However, we show that by utilizing the new conservation theorem and the partial Lagrangian approach one can construct a number of local and nonlocal conservation laws for the underlying equation. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：3081 / 3089

页数：9

共 20 条

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