文献类型：期刊文献

中文题名：Explicit solutions from residual symmetry of the Boussinesq equation

英文题名：Explicit solutions from residual symmetry of the Boussinesq equation

作者：Liu Xi-Zhong[1];Jun, Yu[1];Bo, Ren[1]

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

年份：2015

卷号：0

期号：3

中文期刊名：中国物理B：英文版

外文期刊名：CHINESE PHYSICS B

收录：SCI-EXPANDED(收录号：WOS:000351056400002)、CSTPCD、、EI(收录号：20151000593084)、CSCD2015_2016、Scopus(收录号：2-s2.0-84923795976)、WOS、CSCD

基金：Project supported by the National Natural Science Foundation of China (Grant Nos. 11347183, 11405110, 11275129, and 11305106) and the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y7080455 and LQ13A050001).

语种：英文

中文关键词：Boussinesq方程;对称性;残余;非线性方程;非线性波;本地化;点对称;相似度

外文关键词：Boussinesq equation; localization procedure; residual symmetry; symmetry reduction solution

中文摘要：The Bcklund transformation related symmetry is nonlocal, which is hard to be applied in constructing solutions for nonlinear equations. In this paper, the residual symmetry of the Boussinesq equation is localized to Lie point symmetry by introducing multiple new variables. By applying the general Lie point method, two main results are obtained: a new type of Backlund transformation is derived, from which new solutions can be generated from old ones; the similarity reduction solutions as well as corresponding reduction equations are found. The localization procedure provides an effective way to investigate interaction solutions between nonlinear waves and solitons.

外文摘要：The Backlund transformation related symmetry is nonlocal, which is hard to be applied in constructing solutions for nonlinear equations. In this paper, the residual symmetry of the Boussinesq equation is localized to Lie point symmetry by introducing multiple new variables. By applying the general Lie point method, two main results are obtained: a new type of Backlund transformation is derived, from which new solutions can be generated from old ones; the similarity reduction solutions as well as corresponding reduction equations are found. The localization procedure provides an effective way to investigate interaction solutions between nonlinear waves and solitons.