Geodesic
On integrable non--autonomous Li\'{e}nard--type equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 2, pp. 328-340

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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.
Mots-clés : Liénard-type equation, nonlocal transformation, Painlevé–Gambier equation.
Keywords: general solution 
@article{TMF_2018_196_2_a8,
     author = {D. I. Sinelshchikov and N. A. Kudryashov},
     title = {On integrable non--autonomous {Li\'{e}nard--type} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {328--340},
     publisher = {mathdoc},
     volume = {196},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_196_2_a8/}
}
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D. I. Sinelshchikov; N. A. Kudryashov. On integrable non--autonomous Li\'{e}nard--type equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 2, pp. 328-340. http://geodesic.mathdoc.fr/item/TMF_2018_196_2_a8/