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arXiv · 1702.02781

Darboux solutions of non-abelian quantum Painlev\'e II equation in terms of quasideterminants

Irfan Mahmood
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Abstract

In this article non-abelian version of quantum Painlev\'e II equation is presented with Its quasideterminant solutions has been derived by using the Darboux transformations. This non-abelian quantum Painlev\'e II equation may be considered as a specific case of its purely noncommutatie analogue presented by V. Retakh and V. Rubtsov . In these computations the quantum Painlev\'e II symmetric form with commutation relations presented by H. Nagoya are applied to derive Nonabelian quantum Painlev\'e II equation and a new commutation relation between variable $z$ and the solution $ f(z)$ such as $ z f - f z = \frac{1}{2} i \hbar f $ is presented. Finally, the Darboux solutions of that system are generalized to the $N$-th form in terms of quasideterminants.

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Irfan Mahmood. 2017-02-09. Darboux solutions of non-abelian quantum Painlev\'e II equation in terms of quasideterminants. https://arxiv.org/abs/1702.02781

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