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

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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 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.

Original language	English
Pages (from-to)	685-696
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	421
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.07.040
State	Published - 1 Jan 2015

Keywords

Bäcklund transformation
Local and nonlocal conservation law
Nonlocal symmetry
Sine-Gordon equation

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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",

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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

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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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Keywords

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