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

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

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