Nonlocal symmetries and conservation laws of the Sinh-Gordon equation |
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Authors: | Xiao-yan Tang Zu-feng Liang |
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Affiliation: | 1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China;2. Department of Physics, Hangzhou Normal University, Hangzhou 310036, China |
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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. |
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Keywords: | Nonlocal symmetry Nonlocal conservation law Bäcklund transformation Sinh-Gordon equation 70S10 35Q53 76M60 |
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