Darboux solutions of non-abelian quantum Painlevé II equation in terms of quasideterminants

Abstract

In this article non-abelian version of quantum Painlevé II equation is presented with Its quasideterminant solutions has been derived by using the Darboux transformations. This non-abelian quantum Painlevé 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 Painlevé II symmetric form with commutation relations presented by H. Nagoya are applied to derive Nonabelian quantum Painlevé II equation and a new commutation relation between variable $z$ and the solution $f(z)$ such as $zf-fz=\frac{1}{2}i\hslash f$ is presented. Finally, the Darboux solutions of that system are generalized to the $N$-th form in terms of quasideterminants.

arXiv admin note: text overlap with arXiv:1402.3540, arXiv:1201.0900