Nonlocal symmetry,optimal systems,and explicit solutions of the mKdV equation |
| |
Authors: | Xin Xiang-Peng Miao Qian Chen Yong |
| |
Institution: | Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China |
| |
Abstract: | 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. |
| |
Keywords: | nonlocal symmetry optimal system prolonged system explicit solutions |
本文献已被 CNKI 维普 等数据库收录! |
| 点击此处可从《中国物理 B》浏览原始摘要信息 |
| 点击此处可从《中国物理 B》下载免费的PDF全文 |
|