Nonlocal symmetries and conservation laws of the Sinh-Gordon equation

被引：9

作者：

Tang, Xiao-yan ^{[1
]}

Liang, Zu-feng ^{[2
]}

机构：

[1] East China Normal Univ, Shanghai Key Lab Trustworthy Comp, Shanghai 200062, Peoples R China

[2] Hangzhou Normal Univ, Dept Phys, Hangzhou 310036, Zhejiang, Peoples R China

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2017年 / 24卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Nonlocal symmetry; Nonlocal conservation law; Backlund transformation; Sinh-Gordon equation; SIMILARITY REDUCTIONS; BOUSSINESQ EQUATION; INTEGRABLE SYSTEMS; KDV EQUATIONS; KP HIERARCHY; CONSTRAINTS; TRANSFORMATIONS;

D O I：

10.1080/14029251.2017.1282246

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Nonlocal symmetries of the (1 + 1)-dimensional Sinh-Gordon (ShG) equation are obtained by requiring it, together with its Backlund transformation (BT), to be form invariant under the infinitesimal transformation. Naturally, the spectrum parameter in the BT enters the nonlocal symmetries, and thus through the parameter expansion procedure, infinitely many nonlocal symmetries of the ShG equation can be generated accordingly. Making advantages of the consistent conditions introduced when solving the nonlocal symmetires, some new nonlocal conservation laws of the ShG equation related to the nonlocal symmetries are obtained straightforwardly. Finally, taking the nonlocal symmetries as symmetry constraint conditions imposing on the BT, some new finite and infinite dimensional nonlinear systems are constructed.

引用

页码：93 / 106

页数：14

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