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

Liu, Hanze; Li, Jibin; Zhang, Quanxin

J. Comput. Appl. Math. 228, No. 1, 1-9 (2009).

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

Keywords:

general Burgers’ equation; Lie symmetry analysis; similarity reduction; exact solution

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