新的修正VN方程组的对称、约化和精确解  

Lie Symmetries and Exact Solutions of a New Modified VN System

作　　者：刘庆松[1] 

机构地区：[1]聊城大学学报编辑部,山东聊城252059

出　　处：《河北师范大学学报（自然科学版）》2016年第4期277-285,共9页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11076015)

摘　　要：利用改进的CK直接方法 ,研究了修正VN方程组,建立了该方程组新、旧解之间的关系,基于此关系推广了方程组的解.同时,得到了该方程组的对称和约化,通过求解约化方程,得到修正的VN方程组许多新的精确解,包括幂级数解、艾米尔函数解、雅克比椭圆函数解等.In this paper,we study the modified VN system by using an improved direct CK method,a relationship is constructed between the new solutions and the old ones of the modified VN system.Based on the relationship,new solutions are obtained by using agiven solution of the equation.At the same time,the symmetry of the modified VN system is also obtained.By solving the reduction equation,some kinds of explicit solutions of the modified VN system are obtained,including the power series solution,the Airy function solution and Jacobi elliptic function solution.

关 键 词：改进的CK直接方法 修正的VN方程组 对称 约化 精确解 

分 类 号：O175.2[理学—数学]