Infinitely many nonlocal symmetries and conservation laws for the (1+1)-dimensional Sine-Gordon equation

Jian yong Wang; Xiao yan Tang; Zu feng Liang; Sen yue Lou

doi:10.1016/j.jmaa.2014.07.040

Infinitely many nonlocal symmetries and conservation laws for the (1+1)-dimensional Sine-Gordon equation

Jian yong Wang
, Xiao yan Tang
, Zu feng Liang^*
, Sen yue Lou

^*此作品的通讯作者

数学科学学院

Shanghai Jiao Tong University
Ningbo University
Hangzhou Normal University
East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

10 引用（Scopus）

摘要

Infinitely many nonlocal symmetries and infinitely many local and nonlocal conservation laws of the (1. +. 1)-dimensional Sine-Gordon (SG) equation are derived in terms of its Bäcklund transformation (BT). Some special nonlocal symmetries and nonlocal conservation laws are obtained from the linearized equations of the SG equation and its BT. Furthermore, one can derive infinitely many nonlocal symmetries from a known nonlocal symmetry, but also infinitely many nonlocal conservation laws from a known nonlocal conservation law. In addition, infinitely many local and nonlocal conservation laws can be directly generated from the BT through the parameter expansion procedure.

源语言	英语
页（从-至）	685-696
页数	12
期刊	Journal of Mathematical Analysis and Applications
卷	421
期	1
DOI	https://doi.org/10.1016/j.jmaa.2014.07.040
出版状态	已出版 - 1 1月 2015

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10.1016/j.jmaa.2014.07.040

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title = "Infinitely many nonlocal symmetries and conservation laws for the (1+1)-dimensional Sine-Gordon equation",

abstract = "Infinitely many nonlocal symmetries and infinitely many local and nonlocal conservation laws of the (1. +. 1)-dimensional Sine-Gordon (SG) equation are derived in terms of its B{\"a}cklund transformation (BT). Some special nonlocal symmetries and nonlocal conservation laws are obtained from the linearized equations of the SG equation and its BT. Furthermore, one can derive infinitely many nonlocal symmetries from a known nonlocal symmetry, but also infinitely many nonlocal conservation laws from a known nonlocal conservation law. In addition, infinitely many local and nonlocal conservation laws can be directly generated from the BT through the parameter expansion procedure.",

keywords = "B{\"a}cklund transformation, Local and nonlocal conservation law, Nonlocal symmetry, Sine-Gordon equation",

author = "Wang, \{Jian yong\} and Tang, \{Xiao yan\} and Liang, \{Zu feng\} and Lou, \{Sen yue\}",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

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doi = "10.1016/j.jmaa.2014.07.040",

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T1 - Infinitely many nonlocal symmetries and conservation laws for the (1+1)-dimensional Sine-Gordon equation

AU - Wang, Jian yong

AU - Tang, Xiao yan

AU - Liang, Zu feng

AU - Lou, Sen yue

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Infinitely many nonlocal symmetries and infinitely many local and nonlocal conservation laws of the (1. +. 1)-dimensional Sine-Gordon (SG) equation are derived in terms of its Bäcklund transformation (BT). Some special nonlocal symmetries and nonlocal conservation laws are obtained from the linearized equations of the SG equation and its BT. Furthermore, one can derive infinitely many nonlocal symmetries from a known nonlocal symmetry, but also infinitely many nonlocal conservation laws from a known nonlocal conservation law. In addition, infinitely many local and nonlocal conservation laws can be directly generated from the BT through the parameter expansion procedure.

AB - Infinitely many nonlocal symmetries and infinitely many local and nonlocal conservation laws of the (1. +. 1)-dimensional Sine-Gordon (SG) equation are derived in terms of its Bäcklund transformation (BT). Some special nonlocal symmetries and nonlocal conservation laws are obtained from the linearized equations of the SG equation and its BT. Furthermore, one can derive infinitely many nonlocal symmetries from a known nonlocal symmetry, but also infinitely many nonlocal conservation laws from a known nonlocal conservation law. In addition, infinitely many local and nonlocal conservation laws can be directly generated from the BT through the parameter expansion procedure.

KW - Bäcklund transformation

KW - Local and nonlocal conservation law

KW - Nonlocal symmetry

KW - Sine-Gordon equation

UR - https://www.scopus.com/pages/publications/84925751963

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DO - 10.1016/j.jmaa.2014.07.040

M3 - 文章

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SN - 0022-247X

VL - 421

SP - 685

EP - 696

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Infinitely many nonlocal symmetries and conservation laws for the (1+1)-dimensional Sine-Gordon equation

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