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Group classification of systems of nonlinear reaction-diffusion equations with triangular diffusion matrix. (English) Zbl 1128.35055
Ukr. Mat. Zh. 59, No. 3, 395-411 (2007) and in Ukr. Math. J. 59, No. 3, 439-458 (2007).
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.

35K57 Reaction-diffusion equations
58J70 Invariance and symmetry properties for PDEs on manifolds
35A30 Geometric theory, characteristics, transformations in context of PDEs
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