Abstract
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.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 196, No. 2, pp. 328–340, August, 2018.
This research is supported by a grant from the Russian Science Foundation (Project No. 17-71-10241).
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Sinelshchikov, D.I., Kudryashov, N.A. Integrable Nonautonomous Liénard-Type Equations. Theor Math Phys 196, 1230–1240 (2018). https://doi.org/10.1134/S0040577918080093
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DOI: https://doi.org/10.1134/S0040577918080093