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Lie group classification of a generalized Lane-Emden type system in two dimensions. (English) Zbl 1282.35019
Summary: The aim of this work is to perform a complete Lie symmetry classification of a generalized Lane-Emden type system in two dimensions which models many physical phenomena in biological and physical sciences. The classical approach of group classification is employed for classification. We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.

MSC:
35A30Geometric theory for PDE, characteristics, transformations
35J91Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
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References:
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