(2+1)维广义浅水波方程的非局部对称及精确解  

Nonlocal Symmetries and Exact Solutions of a Generalized(2 +1)-Dimensional Shallow Water Wave Equation

作　　者：张琳琳[1] 吕海玲 ZHANG Lin-lin;LV Hai-ling(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China;Zaozhuang University,Zaozhuang 277160,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059 [2]枣庄学院,山东枣庄277160

出　　处：《枣庄学院学报》2019年第5期53-58,共6页Journal of Zaozhuang University

基　　金：国家自然科学基金资助项目(项目编号:11505090)

摘　　要：本文利用截断Painlevé分析,研究了(2+1)维广义浅水波方程的Schwartzian形式,并通过方程的Lax对构造了此方程的非局部对称.通过引入新的变量,将非局部对称延拓成封闭的局域系统,利用封闭系统的Lie对称,成功地构造了群不变解,并利用得到的Lie对称,约化求解原方程,得到了方程的特殊类型的精确解,即孤立子解与椭圆周期波解的相互作用解,为解释浅水波中的一些非线性现象提供了科学依据.In this paper,the Schwartzian form of the (2+1)dimensional generalized shallow water wave equation is studied by using the truncated Painlevé analysis,and the nonlocal symmetres of the equation are constructed by using the Lax pair of the equation.By introducing a new variable,nonlocal symmetry is converted into a closed system.Furthermore,using the Lie point symmetries of the closed system and Schwartzian equation,some exact interaction solutions are obtained,such as soliton-cnoidal wave solutions which can be used to explain the nonlinear phenomenon in shallow water wave.

关 键 词：非局部对称 截断Painlevé分析 相互作用解 

分 类 号：O175.29[理学—数学]