Nonlocal symmetry, optimal systems, and explicit solutions of the mKdV equation  

作　　者：辛祥鹏 苗倩 陈勇 

机构地区：[1]Shanghai Key Laboratory of Trustworthy Computing, East China Normal University

出　　处：《Chinese Physics B》2014年第1期49-54,共6页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11075055 and 11275072);the Innovative Research Team Program of the National Natural Science Foundation of China(Grant No.61021004);the National High Technology Research and Development Program of China(Grant No.2011AA010101);the Shanghai Knowledge Service Platform for Trustworthy Internet of Things,China(Grant No.ZF1213)

摘　　要：The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties.The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties.

关 键 词：nonlocal symmetry optimal system prolonged system explicit solutions 

分 类 号：O175[理学—数学]