Conditional Lie-Bäcklund Symmetry and New Variable Separation Solutions of the Third Order KdV-Type Equations |
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| Authors: | Gai-Zhu Qu Shun-Li Zhang Hai-Xia Li Gang-Wei Wang |
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| Institution: | 1. School of Mathematics and Physics, Weinan Normal University, Weinan 714000, China;
2. Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi'an 710069, China;
3. Institute of Mathematics Science, Baoji University of Arts and Sciences, Baoji 721013, China;
4. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China |
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| Abstract: | The functionally generalized variable separation solutions of a general KdV-type equations ut=uxxx + A(u, ux)uxx + B(u, ux) are investigated by developing the conditional Lie-Bäcklund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-Bäcklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations. |
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| Keywords: | KdV-type equation conditional Lie-Bäcklund symmetry invariant subspace functionally generalized separation solutions dynamical system |
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