Abstract
We study a family of nonautonomous generalized Lienard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painleve–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Lienard-type equations. We demonstrate that these criteria can be used to construct general traveling-wave and stationary solutions of certain classes of diffusion–convection equations. We also illustrate our results with several other examples of integrable nonautonomous Lienard-type equations.
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