# Lax pair representation and Darboux transformation of noncommutative Painlevé’s second equation

@article{Irfan2012LaxPR, title={Lax pair representation and Darboux transformation of noncommutative Painlev{\'e}’s second equation}, author={Muhammad Irfan}, journal={Journal of Geometry and Physics}, year={2012}, volume={62}, pages={1575-1582} }

## 9 Citations

Quasideterminant solutions of NC Painlevé II equation with the Toda solution at n=1 as a seed solution in its Darboux transformation

- Mathematics
- 2014

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

- Mathematics
- 2017

In this article non-abelian version of quantum Painleve II equation is presented with Its quasideterminant solutions has been derived by using the Darboux transformations. This non-abelian quantum…

Zero curvature representation of non-commutative and quantum Painlev\'e II equation with its non-vacuum solutions

- Mathematics, Physics
- 2014

Quasideterminant Darboux solutions of Noncommutative Equations of Langmuir Oscillations

- Mathematics
- 2021

This article encloses some results on nonncommutative analogue of nonabelian equations of Langmuir oscillations. One of the main contributions of this work is to construct the Darbboux transformation…

Darboux transformation and exact solitonic solutions of integrable coupled nonlinear wave equation

- Mathematics
- 2022

In this article, we construct the Darboux solutions of integrable coupled nonlinear wave equation associated with Hirota Satsuma system in Darboux framework with their N-th generalization in terms of…

Matrix Painlevé II equations

- Physics, Mathematics
- 2020

Abstract We use the Painlevé–Kovalevskaya test to find three matrix versions of the Painlevé II equation. We interpret all these equations as group-invariant reductions of integrable matrix evolution…

On matrix Painlev\'e-4 equations. Part 2: Isomonodromic Lax pairs

- Physics
- 2021

For all non-equivalent matrix systems of Painlevé-4 type found by authors in [4], isomonodromic Lax pairs are presented. Limiting transitions from these systems to matrix Painlevé-2 equations are…

A new stochastic computing paradigm for nonlinear Painlevé II systems in applications of random matrix theory

- Computer Science
- 2018

Abstract.The aim of the present work is to investigate the stochastic numerical solutions of nonlinear Painlevé II systems arising from studies of two-dimensional Yang-Mills theory, growth processes…

S I ] 2 3 O ct 2 02 1 On matrix Painlevé-4 equations . Part 2 : Isomonodromic Lax pairs

- Physics
- 2021

For all non-equivalent matrix systems of Painlevé-4 type found by authors in [4], isomonodromic Lax pairs are presented. Limiting transitions from these systems to matrix Painlevé-2 equations are…

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