New variable separation approach: application to nonlinear diffusion equations

Details New variable separation approach: application to nonlinear diffusion equations New variable separation approach: application to nonlinear diffusion equations

2002-10-09

arxiv.org/abs/nlin/0210017v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, 2 figs

Scientific paper

10.1088/0305-4470/36/49/006

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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