Zero curvature representation of non-commutative and quantum Painlevé II equation with its non-vacuum solutions

Irfan Mahmood (1, 2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 University of the Pun jab

In this paper, I derive a zero curvature representation of quantum Painlevé II equation and its Riccati form which can be reduced to the classical Painlevé II when ħ→0. Further I derive non-vacuum solitonic esolutions of the noncommutative Painlevé II equation with the help of its Darboux transformation for which the solution of the noncommutative Painlevé Riccati equation has been taken as a seed solution.

Mots clés: Integrable systems; Painlevé II equation; zero curvature condition; Riccati equation; Darboux transformation.

Mots clés: Darboux transformation

Domaines: Physique mathématique [math-ph]

Irfan Mahmood. Zero curvature representation of non-commutative and quantum Painlevé II equation with its non-vacuum solutions. 2014. ⟨hal-00950582⟩