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Similarity reductions and Painlevé property of the coupled higher dimensional Burgers’ equation. (English) Zbl 0755.35122

Summary: Using the Lie’s infinitesimal group analysis, we derive a large class of similarity solutions for the coupled (2+1) dimensional Burgers’ equation. The systematic study of the Lie symmetries for this system leads to a class of nonlinear ordinary differential equations through similarity variables at two stages of reduction. Furthermore, the structure of the infinitesimal generators of the Lie group suggests the existence of an eight-dimensional Lie algebra. We analyse the nature of this Lie algebra. Also, we notice that the system does not admit the generalized Painlevé property. On the other hand, the ordinary differential equations obtained by the above process possess the Painlevé property for certain cases.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
58J70 Invariance and symmetry properties for PDEs on manifolds
35A30 Geometric theory, characteristics, transformations in context of PDEs
54H15 Transformation groups and semigroups (topological aspects)
22E05 Local Lie groups
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