文献类型：期刊文献

英文题名：New interaction solutions from residual symmetry reduction and consistent Riccati expansion of the (2+1)-dimensional Boussinesq equation

作者：Liu, Xi-zhong[1];Yu, Jun[1];Lou, Zhi-Mei[1]

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

年份：2018

卷号：92

期号：4

起止页码：1469

外文期刊名：NONLINEAR DYNAMICS

收录：SCI-EXPANDED(收录号：WOS:000431789700002)、、EI(收录号：20180804815067)、Scopus(收录号：2-s2.0-85042117513)、WOS

基金：The authors are grateful to the referee, whose suggestions for the paper have led to a substantial clarification of our work. This work was supported by the National Natural Science Foundation of China under Grant Nos. 11405110, 11275129, 11472177 and the Natural Science Foundation of Zhejiang Province of China under Grant No. LY18A050001.

语种：英文

外文关键词：(2+1)-dimensional Boussinesq equation; Residual symmetry; Consistent Riccati expansion

外文摘要：In this paper, the (2 + 1)-dimensional Boussinesq equation is studied by applying residual symmetry reduction method and consistent Riccati expansion (CRE) method, respectively. By introducing multiple new dependent variables to enlarge the (2 + 1)-dimensional Boussinesq system, the residual symmetry is localized and the corresponding finite transformation is obtained by using Lie's first theorem. The symmetry reduction solutions related to the residual symmetry of the (2 + 1)-dimensional Boussinesq equation is obtained by using the standard Lie symmetry method, which includes complicated interaction models. Furthermore, the (2 + 1)-dimensional Boussinesq equation is found to have CRE integrability, and new Backlund transformations (BTs) are consequently obtained. New interaction solutions are obtained from these BTs; particularly, the interaction solution between soliton and background cnoidal wave is given and analyzed explicitly.