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Symmetry groups of differential-difference equations and their compatibility |
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| Authors: | Shoufeng Shen Changzheng Qu |
| Institution: | a Center for Nonlinear Studies, Northwest University, Xi'an 710069, China b Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China c Department of Mathematics, Northwest University, Xi'an 710069, China |
| Abstract: | It is shown that the intrinsic determining equations of a given differential-difference equation (DDE) can be derived by the compatibility between the original equation and the intrinsic invariant surface condition. The (2+1)-dimensional Toda lattice, the special Toda lattice and the DD-KP equation serving as examples are used to illustrate this approach. Then, Bäcklund transformations of the (2+1)-dimensional DDEs including the special Toda lattice, the modified Toda lattice and the DD-KZ equation are presented by using the non-intrinsic direct method. In addition, the Clarkson-Kruskal direct method is developed to find similarity reductions of the DDEs. |
| Keywords: | Symmetry Differential-difference equation Compatibility Bä cklund transformation |
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