Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations with power nonlinearities
Date
2007ISSN
0022-247XSource
Journal of Mathematical Analysis and ApplicationsVolume
330Issue
2Pages
1363-1386Google Scholar check
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A class of variable coefficient (1 + 1)-dimensional nonlinear reaction-diffusion equations of the general form f (x) ut = (g (x) un ux)x + h (x) um is investigated. Different kinds of equivalence groups are constructed including ones with transformations which are nonlocal with respect to arbitrary elements. For the class under consideration the complete group classification is performed with respect to convenient equivalence groups (generalized extended and conditional ones) and with respect to the set of all local transformations. Usage of different equivalences and coefficient gauges plays the major role for simple and clear formulation of the final results. The corresponding set of admissible transformations is described exhaustively. Then, using the most direct method, we classify local conservation laws. Some exact solutions are constructed by the classical Lie method. © 2006 Elsevier Inc. All rights reserved.