New variable separation solutions for the generalized nonlinear diffusion equations |
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Institution: | 1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China;2. Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi'an 710069, China |
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Abstract: | The functionally generalized variable separation of the generalized nonlinear diffusion equations ut=A(u,ux)uxx+ B(u,ux) is studied by using the conditional Lie-Bäcklund symmetry method. The variant forms of the considered equations, which admit the corresponding conditional Lie-Bäcklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided. |
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Keywords: | conditional Lie-Bäcklund symmetry functionally generalized separable solution generalized nonlinear diffusion equation invariant subspace |
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