Non-trivial Darboux solutions of Classical Painlevé second equation

Abstract

In this article an other equivalent linear representation of classical Painlevé 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 Painlevé second equation which are further generalized to the $N$-th form in terms of Wranskian. Finally we present the exact solutions of that equation through its associated Riccati system.

arXiv commentI am updating this paper with addition of some propositions

References in corpus (1)

• Existence and Uniqueness of Tri-tronquée Solutions of the second Painlevé hierarchy