2018/06/07 by Irfan Mahmood, Mahmood, Irfan
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1806.02584
openalex publication_date 2018/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.