文献类型：期刊文献

英文题名：Symmetry reduction related with nonlocal symmetry for Gardner equation

作者：Ren, Bo[1]

机构：[1]Shaoxing Univ, Inst Nonlinear Sci, Shaoxing 312000, Peoples R China

年份：2017

卷号：42

起止页码：456

外文期刊名：COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

收录：SCI-EXPANDED(收录号：WOS:000381584600036)、、EI(收录号：20162502511403)、Scopus(收录号：2-s2.0-84974603718)、WOS

基金：This work was supported by the National Natural Science Foundation of China under Grant No. 11305106.

语种：英文

外文关键词：Gardner equation; Nonlocal symmetry; Symmetry reduction; Interaction solution

外文摘要：Based on the truncated Painleve method or the Mobious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painleve II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways. (C) 2016 Elsevier B.V. All rights reserved.