Painlevé analysis, Lie symmetries, and exact solutions for the time-dependent coefficients Gardner equations

摘要

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. Keywords Variable-coefficient Gardner equation - Painlevé analysis - Lie symmetry analysis - Exact solution This work is supported by the Natural Science Foundation of China (No. 10671179 and No. 10771196), the Natural Science Foundation of Binzhou University (Bzxykj0806).