Nonlocal Symmetries and Explicit Solutions of the Boussinesq Equation

作     者：Xiangpeng XIN Junchao CHEN Yong CHEN 

作者机构：Shanghai Key Laboratory of Trustworthy Computing East China Normal University 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2014年第35卷第6期

页      面：841-856页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.11275072,11435005) the Research Fund for the Doctoral Program of Higher Education of China(No.20120076110024) the Innovative Research Team Program of the National Natural Science Foundation of China(No.61321064) the Shanghai Knowledge Service Platform for Trustworthy Internet of Things(No.ZF1213) the Shanghai Minhang District Talents of High Level Scientific Research Project and the Talent Fund K.C.Wong Magna Fund in Ningbo University 

主　　题：Nonlocal symmetry Lax pair Prolonged system Explicit solution 

摘      要：The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlev~ equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.