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Lie symmetry analysis and exact explicit solutions for general Burgers’ equation. (English) Zbl 1166.35033

Summary: The Lie symmetry analysis is performed for the general Burgers’ equation. The exact solutions and similarity reductions generated from the symmetry transformations are provided. Furthermore, the all exact explicit solutions and similarity reductions based on the Lie group method are obtained, some new method and techniques are employed simultaneously. Such exact explicit solutions and similarity reductions are important in both applications and the theory of nonlinear science.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q35 PDEs in connection with fluid mechanics
35C10 Series solutions to PDEs
22E70 Applications of Lie groups to the sciences; explicit representations
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