Abstract:
Nonlinear differential equations associated with the second Painlevé equation are considered. Transformations for solutions of the singular manifold equation are presented. It is shown that rational solutions of the singular manifold equation are determined by means of the Yablonskii – Vorob'ev polynomials. It is demonstrated that rational solutions for some differential equations are also expressed via the Yablonskii – Vorob'ev polynomials.
Citation:
Nikolay A. Kudryashov, “Rational Solutions of Equations Associated with the Second Painlevé Equation”, Regul. Chaotic Dyn., 25:3 (2020), 273–280
\Bibitem{Kud20}
\by Nikolay A. Kudryashov
\paper Rational Solutions of Equations Associated with the Second Painlevé Equation
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 3
\pages 273--280
\mathnet{http://mi.mathnet.ru/rcd1063}
\crossref{https://doi.org/10.1134/S156035472003003X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000536729000003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85085544274}
Linking options:
https://www.mathnet.ru/eng/rcd1063
https://www.mathnet.ru/eng/rcd/v25/i3/p273
This publication is cited in the following 4 articles:
Sandeep Malik, Sachin Kumar, Anjan Biswas, Yakup Y{\i}ld{\i}r{\i}m, Luminita Moraru, Simona Moldovanu, Catalina Iticescu, Seithuti P. Moshokoa, Dorin Bibicu, Abdulaziz Alotaibi, “Gap Solitons in Fiber Bragg Gratings Having Polynomial Law of Nonlinear Refractive Index and Cubic–Quartic Dispersive Reflectivity by Lie Symmetry”, Symmetry, 15:5 (2023), 963
Anjan Biswas, Jose Vega-Guzman, Abdul H. Kara, Salam Khan, Houria Triki, O. González-Gaxiola, Luminita Moraru, Puiu Lucian Georgescu, “Optical Solitons and Conservation Laws for the Concatenation Model: Undetermined Coefficients and Multipliers Approach”, Universe, 9:1 (2022), 15
Anjan Biswas, Abdul H. Kara, Mehmet Ekici, Elsayed M. E. Zayed, Abdullah K. Alzahrani, Milivoj R. Belic, “Conservation Laws for Solitons in Magneto-optic Waveguides
with Anti-cubic and Generalized Anti-cubic Nonlinearities”, Regul. Chaotic Dyn., 26:4 (2021), 456–461
E. M. E. Zayed, M. E. M. Alngar, R. M. A. Shohib, S. Khan, A. Biswas, A. Dakova, A. Kh. Alzahrani, M. R. Belic, “Optical soliton perturbation with Kudryashov's law of refractive index by modified sub-ODE approach”, J. Nonlinear Opt. Phys. Mater., 30:01N02 (2021), 2150004
Citation in format AMSBIB
Contact us: