Sudip Garai

    Sarisha, D. H. Road, West Bengal, India 743368
    Diamond Harbour Women's University


    Guha P., Garai S., Choudhury A. G.
    Recently Sinelshchikov et al. [1] formulated a Lax representation for a family of nonautonomous second-order differential equations. In this paper we extend their result and obtain the Lax pair and the associated first integral of a non-autonomous version of the Levinson – Smith equation. In addition, we have obtained Lax pairs and first integrals for several equations of the Painlevé – Gambier list, namely, the autonomous equations numbered XII, XVII, XVIII, XIX, XXI, XXII, XXIII, XXIX, XXXII, XXXVII, XLI, XLIII, as well as the non-autonomous equations Nos. XV and XVI in Ince’s book.
    Keywords: Lax representation, Liénard type equations, Painlevé – Gambier equations, first integrals
    Citation: Guha P., Garai S., Choudhury A. G.,  Lax Pairs and First Integrals for Autonomous and Non-Autonomous Differential Equations Belonging to the Painlevé – Gambier List, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 4, pp.  637-650

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