Abstract
It is well known that rational solutions of the second Painlevé equation (P II) are expressed in terms of logarithmic derivatives of the Yablonskii–Vorob'ev polynomials Q n ( z) which are defined through a second order, bilinear differential-difference equation which is equivalent to the Toda equation. In this Letter, using the Hamiltonian theory for P II, it is shown that Q n ( z) also satisfies a fourth order, bilinear ordinary differential equation and a fifth order, quad-linear difference equation. Further, rational solutions of some ordinary differential equations which are solvable in terms of solutions of P II are also expressed in terms of the Yablonskii–Vorob'ev polynomials.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
