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The phase coordinates transformation in Moyal noncommutative framework 2-dimensional harmonic oscillator and Painlevé second equation
Irfan Mahmood
This work aims to explore the physical application of Moyal noncom- mutative formalism with the the presentation of new transformations which connect the old canonical coordinates…
Quantum Painlevé II Lax Pair and Quantum (Matrix) Analogues of Classical Painlevé II equation
Muhammad Waseem, Irfan Mahmood, Hira Sohail
In this article, we present a new quantum Painlevé II Lax pair which explicitly involves the Planck constant and an arbitrary field variable so these two objects make…
Non-trivial Darboux solutions of Classical Painlevé second equation
Irfan Mahmood
In this article an other equivalent linear representation of classical Painlevé second equation is derived by introducing a gauge transformation to old Lax pair. The new linear sys…
Darboux solutions of non-abelian quantum Painlevé II equation in terms of quasideterminants
Irfan Mahmood
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…
Quantum Painlevé II solution and Approximated analytic solution of the Yukawa Potential
Irfan Mahmood
We show that one dimensional non-stationary Schrödi-nger equation with a specific choice of potential reduces to the quantum Painlevé II equation and the solution of its Riccati fo…
Quasideterminant solutions of NC Painlevé II equation with the Toda solution at as a seed solution in its Darboux transformation
Irfan Mahmood
In this paper, I construct the Darboux transformations for the non-commutative Toda solutions at with the help of linear systems whose compatibility condition yields zero c…
Lax pair representation and Darboux transformation of NC Painlevé-II equation
Irfan Mahmood
The extension of Painlevé equations to noncommutative spaces has been considering extensively in the theory of integrable systems and it is also interesting to explore some remarka…