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 procedur...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.展开更多
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)+3 种基金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 FundK.C.Wong Magna Fund in Ningbo University
文摘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.
