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Painlevé analysis, Lie symmetries, and exact solutions for the time-dependent coefficients gardner equations. (English) Zbl 1183.35236

Summary: In this paper, the three variable-coefficient Gardner (vc-Gardner) equations are considered. By using the Painlevé analysis and Lie group analysis method, the Painlevé properties and symmetries for the equations are obtained. Then the exact solutions generated from the symmetries and Painlevé analysis are presented.

MSC:

35Q51 Soliton equations
76B25 Solitary waves for incompressible inviscid fluids
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