Nonlocal symmetries and conservation laws of the Sinh-Gordon equation. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Tang, Xiao-yan; Liang, Zu-feng
• Is Part Of: Journal of nonlinear mathematical physics. Volume 24:Issue 1(2017)
• Page Start: 93
• Page End: 106
• Publication Date: 2017-01-02
• Subjects: Nonlocal symmetry -- Nonlocal conservation law -- Bäcklund transformation -- Sinh-Gordon equation -- 70S10 -- 35Q53 -- 76M60; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2017.1282246
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : Nonlocal symmetries of the (1+1)-dimensional Sinh-Gordon (ShG) equation are obtained by requiring it, together with its Bäcklund 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.