文献类型：期刊文献

中文题名：Bcklund transformations for the Burgers equation via localization of residual symmetries

英文题名：B?cklund transformations for the Burgers equation via localization of residual symmetries

作者：Liu, Xi-Zhong[1]; Yu, Jun[1]; Ren, Bo[1]; Yang, Jian-Rong[2]

机构：[1] Institute of Nonlinear Science, Shaoxing University, Shaoxing, 312000, China; [2] Department of Physics and Electronics, Shangrao Normal University, Shangrao, 334001, China

年份：2014

卷号：23

期号：11

中文期刊名：中国物理B：英文版

外文期刊名：Chinese Physics B

收录：CSTPCD、、EI(收录号：20144800238645)、Scopus(收录号：2-s2.0-84911453668)、CSCD、CSCD2013_2014

基金：supported by the National Natural Science Foundation of China(Grant Nos.11347183,11275129,11305106,11365017,and 11405110);the Natural Science Foundation of Zhejiang Province of China(Grant Nos.Y7080455 and LQ13A050001)

语种：英文

中文关键词：Burgers方程;对称性;本地化;残留;线性叠加;残余;定理

外文关键词：Linear transformations - Mathematical transformations

中文摘要：We obtain the non-local residual symmetry related to truncated Painlev′e expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation into a new system.By using Lie's first theorem, we obtain the finite transformation for the localized residual symmetry. More importantly,we also localize the linear superposition of multiple residual symmetries to find the corresponding finite transformations.It is interesting to find that the n-th B¨acklund transformation for Burgers equation can be expressed by determinants in a compact way.

外文摘要：We obtain the non-local residual symmetry related to truncated Painlevé expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation into a new system. By using Lie's first theorem, we obtain the finite transformation for the localized residual symmetry. More importantly, we also localize the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the n-th B?cklund transformation for Burgers equation can be expressed by determinants in a compact way. ? 2014 Chinese Physical Society and IOP Publishing Ltd.