RLW-KdV方程的对称约化、精确解和守恒律  

Symmetry Reductions, Exact Equations and the Conservation Laws of the Rlw-Kdv Equation

作　　者：李志强[1] 刘汉泽[1] 辛祥鹏[1] LI ZHIQIANG;LIU HANZE;XIN XIANGPENG(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,Chin)

机构地区：[1]聊城大学数学科学学院

出　　处：《应用数学学报》2018年第4期540-549,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11171041,11505090)资助项目

摘　　要：运用经典李群方法研究了正则长波-KdV方程,得到所有的向量场.然后,将正则长波-KdV方程约化成常微分方程,进一步利用e-φ（ε））展开法和Lambert W函数法求精确解.最后,利用李点对称求正则长波-KdV方程的伴随方程和守恒律.In this paper, the regularized long wave-KdV equation is studied. First, using the classical Lie symmetry method, all vector fields and symmetry reduction of the equation with nonlinearity are constructed. Then, the exact traveling wave solutions is provided by using traveling wave transformation, the homogeneous balance principle and e-φ（￡）-expansion method, include the trigonometric function solution, the hyperbolic function solution and the rational function solution. In addition, the new exact solution are obtained the lain- bertW function method, Finally, adjoint equation, Lagiangian and conservation laws of the regularized long wave-KdV equation are derived.

关 键 词：经典李群方法 正则长波-KdV方程 精确解 守恒律 

分 类 号：O175.2[理学—数学]