Infinitely many nonlocal symmetries and nonlocal conservation laws of the integrable modified KdV-sine-Gordon equation

Zu Feng Liang; Xiao Yan Tang; Wei Ding

doi:10.1088/1572-9494/abe9ad

Infinitely many nonlocal symmetries and nonlocal conservation laws of the integrable modified KdV-sine-Gordon equation

Zu Feng Liang
, Xiao Yan Tang
, Wei Ding

School of Mathematical Sciences

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

6 Scopus citations

Abstract

Nonlocal symmetries related to the B cklund transformation (BT) for the modified KdV-sine-Gordon (mKdV-SG) equation are obtained by requiring the mKdV-SG equation and its BT form invariant under the infinitesimal transformations. Then through the parameter expansion procedure, an infinite number of new nonlocal symmetries and new nonlocal conservation laws related to the nonlocal symmetries are derived. Finally, several new finite and infinite dimensional nonlinear systems are presented by applying the nonlocal symmetries as symmetry constraint conditions on the BT.

Original language	English
Article number	055003
Journal	Communications in Theoretical Physics
Volume	73
Issue number	5
DOIs	https://doi.org/10.1088/1572-9494/abe9ad
State	Published - May 2021

Keywords

Nonlocal conservation law
Nonlocal symmetry
The modified KdV-sine-Gordon equation

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10.1088/1572-9494/abe9ad

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title = "Infinitely many nonlocal symmetries and nonlocal conservation laws of the integrable modified KdV-sine-Gordon equation",

abstract = "Nonlocal symmetries related to the B cklund transformation (BT) for the modified KdV-sine-Gordon (mKdV-SG) equation are obtained by requiring the mKdV-SG equation and its BT form invariant under the infinitesimal transformations. Then through the parameter expansion procedure, an infinite number of new nonlocal symmetries and new nonlocal conservation laws related to the nonlocal symmetries are derived. Finally, several new finite and infinite dimensional nonlinear systems are presented by applying the nonlocal symmetries as symmetry constraint conditions on the BT.",

keywords = "Nonlocal conservation law, Nonlocal symmetry, The modified KdV-sine-Gordon equation",

author = "Liang, \{Zu Feng\} and Tang, \{Xiao Yan\} and Wei Ding",

note = "Publisher Copyright: {\textcopyright} 2021 Institute of Theoretical Physics CAS, Chinese Physical Society and IOP Publishing.",

year = "2021",

month = may,

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T1 - Infinitely many nonlocal symmetries and nonlocal conservation laws of the integrable modified KdV-sine-Gordon equation

AU - Liang, Zu Feng

AU - Tang, Xiao Yan

AU - Ding, Wei

PY - 2021/5

Y1 - 2021/5

N2 - Nonlocal symmetries related to the B cklund transformation (BT) for the modified KdV-sine-Gordon (mKdV-SG) equation are obtained by requiring the mKdV-SG equation and its BT form invariant under the infinitesimal transformations. Then through the parameter expansion procedure, an infinite number of new nonlocal symmetries and new nonlocal conservation laws related to the nonlocal symmetries are derived. Finally, several new finite and infinite dimensional nonlinear systems are presented by applying the nonlocal symmetries as symmetry constraint conditions on the BT.

AB - Nonlocal symmetries related to the B cklund transformation (BT) for the modified KdV-sine-Gordon (mKdV-SG) equation are obtained by requiring the mKdV-SG equation and its BT form invariant under the infinitesimal transformations. Then through the parameter expansion procedure, an infinite number of new nonlocal symmetries and new nonlocal conservation laws related to the nonlocal symmetries are derived. Finally, several new finite and infinite dimensional nonlinear systems are presented by applying the nonlocal symmetries as symmetry constraint conditions on the BT.

KW - Nonlocal conservation law

KW - Nonlocal symmetry

KW - The modified KdV-sine-Gordon equation

UR - https://www.scopus.com/pages/publications/85104226493

U2 - 10.1088/1572-9494/abe9ad

DO - 10.1088/1572-9494/abe9ad

M3 - 文章

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SN - 0253-6102

VL - 73

JO - Communications in Theoretical Physics

JF - Communications in Theoretical Physics

IS - 5

M1 - 055003

ER -

Infinitely many nonlocal symmetries and nonlocal conservation laws of the integrable modified KdV-sine-Gordon equation

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Keywords

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