带强迫项KdV方程的非线性自伴随性和守恒律(英文)  

Nonlinear self-adjointness and conservation laws of forced KdV equation

作　　者：张立华[1] 

机构地区：[1]德州学院数学系,山东德州253023

出　　处：《量子电子学报》2013年第2期154-161,共8页Chinese Journal of Quantum Electronics

基　　金：Supported by the Natural Science Foundation of Shandong Province under Grant ZR2010AL019

摘　　要：应用非线性自伴随性的概念和伊布拉基莫夫的一般守恒律定理,研究了带强迫KdV方程的非线性自伴随性和守恒律。首先讨论了自伴随性,结果表明这个方程具有非线性自伴随性,同时得到了这个方程的形式拉格朗日量。在对此方程进行李对称分析后,根据李对称的不同得到了此方程的一些非平凡守恒律。Using the concept of nonlinear self-adjointness and the general theorem on conservation laws developed by Ibragimov, nonlinear self-adjointness and conservation laws for the forced KdV equation are investigated. Its self-adjointness was disscussed firstly, and it＇s found that the forced KdV equation is nonlinearly self-adjoint. At the same time, formal Lagrangian for the equation is obtained. Having performed Lie symmetry analysis for the equation, lots of nontrivial conservation laws for the equation were derived according to the difference of Lie symmetries

关 键 词：非线性方程 带强迫项的KdV方程 守恒律 李对称 形式拉格朗日量 

分 类 号：O431[机械工程—光学工程]