文献类型：期刊文献

中文题名：Exact solutions and residual symmetries of the Ablowitz–Kaup–Newell–Segur system

英文题名：Exact solutions and residual symmetries of the Ablowitz-Kaup-Newell-Segur system

作者：Liu Ping[1,2];Zeng Bao-Qing[1,2];Yang Jian-Rong[3];Ren Bo[4]

机构：[1]Univ Elect Sci & Technol China, Zhongshan Inst, Coll Electron & Informat Engn, Zhongshan 528402, Peoples R China;[2]Univ Elect Sci & Technol China, Sch Phys Elect, Chengdu 610054, Peoples R China;[3]Shangrao Normal Univ, Dept Phys & Elect, Shangrao 334001, Peoples R China;[4]Shaoxing Univ, Inst Nonlinear Sci, Shaoxing 312000, Peoples R China

年份：2015

卷号：0

期号：1

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:000350701400002)、CSTPCD、、EI(收录号：20150700524086)、CSCD2015_2016、Scopus(收录号：2-s2.0-84922572186)、WOS、CSCD

基金：Project supported by the National Natural Science Foundation of China (Grant Nos. 11305031, 11365017, and 11305106), the Natural Science Foundation of Guangdong Province, China (Grant No. S2013010011546), the Natural Science Foundation of Zhejiang Province, China (Grant No. LQ13A050001), the Science and Technology Project Foundation of Zhongshan, China (Grant Nos. 2013A3FC0264 and 2013A3FC0334), and the Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province, China (Grant No. Yq2013205).

语种：英文

中文关键词：AKNS系统;对称性;残余;向量;AKNS方程;Painlevé分析;Backlund变换;缩放变换

外文关键词：residual symmetries; Ablowitz-Kaup-Newell-Segur equation; exact solution; Backlund transformation

中文摘要：The residual symmetries of the Ablowitz–Kaup–Newell–Segur(AKNS)equations are obtained by the truncated Painleve′analysis.The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries of a prolonged AKNS system.The local Lie point symmetries of the prolonged AKNS equations are composed of the residual symmetries and the standard Lie point symmetries,which suggests that the residual symmetry method is a useful complement to the classical Lie group theory.The calculation on the symmetries shows that the enlarged equations are invariant under the scaling transformations,the space–time translations,and the shift translations.Three types of similarity solutions and the reduction equations are demonstrated.Furthermore,several types of exact solutions for the AKNS equations are obtained with the help of the symmetry method and the Bcklund transformations between the AKNS equations and the Schwarzian AKNS equation.

外文摘要：The residual symmetries of the Ablowitz-Kaup-Newell-Segur (AKNS) equations are obtained by the truncated Painleve analysis. The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries of a prolonged AKNS system. The local Lie point symmetries of the prolonged AKNS equations are composed of the residual symmetries and the standard Lie point symmetries, which suggests that the residual symmetry method is a useful complement to the classical Lie group theory. The calculation on the symmetries shows that the enlarged equations are invariant under the scaling transformations, the space-time translations, and the shift translations. Three types of similarity solutions and the reduction equations are demonstrated. Furthermore, several types of exact solutions for the AKNS equations are obtained with the help of the symmetry method and the Backlund transformations between the AKNS equations and the Schwarzian AKNS equation.