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Group classification of systems of nonlinear reaction-diffusion equations with triangular diffusion matrix. (English) Zbl 1128.35055
Summary: We complete the group classification of systems of two coupled nonlinear reaction-diffusion equations with general diffusion matrix begun in author’s previous works. Namely, all non-equivalent equations with triangular diffusion matrix are classified. In addition, we describe symmetries of diffusion systems with nilpotent diffusion matrix and additional terms with first-order derivatives.

MSC:
35K57Reaction-diffusion equations
58J70Invariance and symmetry properties
35A30Geometric theory for PDE, characteristics, transformations