Non-trivial Darboux solutions of Classical Painlev\'e second equation
Mathematical Physics
2023-05-17 v2 math.MP
Abstract
In this article an other equivalent linear representation of classical Painlev\'e second equation is derived by introducing a gauge transformation to old Lax pair. The new linear system of that equation carries similar structure as other integrable systems possess in AKNS scheme. That system yields non-trivial Darboux solutions of classical Painlev\'e second equation which are further generalized to the -th form in terms of Wranskian. Finally we present the exact solutions of that equation through its associated Riccati system.
Keywords
Cite
@article{arxiv.1806.02584,
title = {Non-trivial Darboux solutions of Classical Painlev\'e second equation},
author = {Irfan Mahmood},
journal= {arXiv preprint arXiv:1806.02584},
year = {2023}
}
Comments
I am updating this paper with addition of some propositions