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Regular version of the site

Article

Integrable Nonautonomous Liénard-Type Equations

Theoretical and Mathematical Physics. 2018. Vol. 196. No. 2. P. 1230-1240.
Sinelshchikov D., Кудряшов Н. А.

We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-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 Liénard-type equations.