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New variable separation approach: application to nonlinear diffusion equations

Shun-li Zhang·Sen-yue Lou·Chang-zheng Qu
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Abstract

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.

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Shun-li Zhang, Sen-yue Lou, Chang-zheng Qu. 2002-10-09. New variable separation approach: application to nonlinear diffusion equations. https://doi.org/10.1088/0305-4470%2F36%2F49%2F006

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