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Group classifications, optimal systems and exact solutions to the generalized Thomas equations. (English) Zbl 1246.35196
Summary: The complete group classifications are performed on the types of Thomas equations (TEs), which arise in the study of chemical exchange progress, etc., all of the vector fields of the equations are presented. Then, the optimal system of the general Thomas equation is given, and all of the symmetry reductions and exact solutions generated from the optimal system are investigated. Furthermore, the exact analytic solutions to the Thomas equations are obtained by the generalized power series method.
MSC:
35Q92PDEs in connection with biology and other natural sciences
35A30Geometric theory for PDE, characteristics, transformations
35C05Solutions of PDE in closed form
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