Abstract
This paper is concerned with the variable-coefficient Gardner (vc-Gardner) types of equations, which arise in fluid dynamics, nonlinear lattice and plasma physics. As its special cases, the generalized cylindrical KdV types of equations are considered simultaneously. By using the combination of Painleve analysis and Lie group classification method, the integrable conditions, Backlund transformations and complete group classifications of the vc-Gardner types of equations are obtained. Then, the exact solutions generated from the Painleve analysis and symmetry reductions are investigated.
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