TY - JOUR
T1 - Lax pairs and first integrals for autonomous and non-autonomous differential equations belonging to the painlevé – Gambier list
AU - Guha, P.
AU - Garai, S.
AU - Choudhury, A. G.
N1 - Publisher Copyright:
© 2020 Institute of Computer Science Izhevsk. All rights reserved.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - Recently Sinelshchikov et al. [1] formulated a Lax representation for a family of non-autonomous 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.
AB - Recently Sinelshchikov et al. [1] formulated a Lax representation for a family of non-autonomous 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.
KW - First integrals
KW - Lax representation
KW - Liénard type equations
KW - Painlevé–Gambier equations
UR - http://www.scopus.com/inward/record.url?scp=85099914329&partnerID=8YFLogxK
U2 - 10.20537/ND200408
DO - 10.20537/ND200408
M3 - Article
AN - SCOPUS:85099914329
SN - 2658-5324
VL - 16
SP - 637
EP - 650
JO - Russian Journal of Nonlinear Dynamics
JF - Russian Journal of Nonlinear Dynamics
IS - 4
ER -