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}
}
  • M. Irfan
  • Published 1 July 2012
  • Mathematics
  • Journal of Geometry and Physics
Darboux solutions of non-abelian quantum Painlev\'e II equation in terms of quasideterminants
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
Quasideterminant Darboux solutions of Noncommutative Equations of Langmuir Oscillations
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
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
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
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
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
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

References

SHOWING 1-10 OF 30 REFERENCES
Towards Noncommutative Integrable Systems
On a direct approach to quasideterminant solutions of a noncommutative KP equation
A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary
Noncommutative Burgers equation
We present a noncommutative version of the Burgers equation which possesses the Lax representation and discuss the integrability in detail. We find a noncommutative version of the Cole–Hopf
Fredholm Determinants and Pole-free Solutions to the Noncommutative Painlevé II Equation
We extend the formalism of integrable operators à la Its-Izergin-Korepin-Slavnov to matrix-valued convolution operators on a semi–infinite interval and to matrix integral operators with a kernel of
Exact Noncommutative KP and KdV Multi-solitons
We derive the Kadomtsev-Petviashvili (KP) equation defined over a general associative algebra and construct its N-soliton solution. For the example of the Moyal algebra, we find multi-soliton
With a Cole–Hopf transformation to solutions of the noncommutative KP hierarchy in terms of Wronski matrices
In the case of the KP hierarchy where the dependent variable takes values in an (arbitrary) associative algebra , it is known that there are solutions which can be expressed in terms of
Noncommutative Generalized NS and Super Matrix KdV Systems from a Noncommutative Version of (Anti-) Self-Dual Yang-Mills Equations
A noncommutative version of the (anti-) self-dual Yang-Mills equations is shown to be related via dimensional reductions to noncommutative formulations of the generalized (SO(3)/SO(2)) nonlinear
Noncommutative integrable field theories in 2d
Darboux transformation of the generalized coupled dispersionless integrable system
The Darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on a non-Abelian Lie group is studied, and the solutions are shown to be expressed in
Darboux Transformations and Solitons
In 1882 Darboux proposed a systematic algebraic approach to the solution of the linear Sturm-Liouville problem. In this book, the authors develop Darboux's idea to solve linear and nonlinear partial
...
...