|
This article is cited in 1 scientific paper (total in 1 paper)
Mathematical problems of nonlinearity
Lax Pairs and First Integrals for Autonomous and Non-Autonomous Differential Equations Belonging to the Painlevé – Gambier List
P. Guhaab, S. Garaic, A. G. Choudhuryc a SN Bose National Centre for Basic Sciences,
JD Block, Sector III, Salt Lake, Kolkata 700106, India
b Department of Mathematics,
Khalifa University, Abu Dhabi, UAE
c Department of Physics, Diamond Harbour Women’s University,
D.H.Road, Sarisha 743368, West Bengal, India
Abstract:
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.
Received: 21.06.2020 Accepted: 17.09.2020
Citation:
P. Guha, S. Garai, A. G. Choudhury, “Lax Pairs and First Integrals for Autonomous and Non-Autonomous Differential Equations Belonging to the Painlevé – Gambier List”, Rus. J. Nonlin. Dyn., 16:4 (2020), 637–650
Linking options:
https://www.mathnet.ru/eng/nd734 https://www.mathnet.ru/eng/nd/v16/i4/p637
|
Statistics & downloads: |
Abstract page: | 107 | Full-text PDF : | 149 | References: | 16 |
|