arXiv subjects

Irfan Mahmood

Publications and source records attributed to Irfan Mahmood.

14 recordsLinked to original sources

arXiv2026

The phase coordinates transformation in Moyal noncommutative framework 2-dimensional harmonic oscillator and Painlevé second equation

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 to purly noncommuting phase coordi- nates through the parameters describe the Moyal noncommutative deforma- tion. These transformations are consistent with the Moyal noncommunica- tive brackets and build sixteen components traceless anti-symmetric tensor. This formalism incorporates space-space and space-momentum noncommu- taivity rather then noncommutativity (Heisenberg quantum commutation ) only for the canonical coordinates. The transformations imply to construct noncommutative analogs of 2-dimensional harmonic oscillator with its superintegrability and Painlevé second equation. The associated deformed Hamiltonians additionally involve some extra symmetries and reveal a deep physical understanding of about the additional symmetries with noncommunicative structure. The Painlevé second noncommutative coordinates transformation are also efficiently applied to generate the first Yablonskii Vorobev polynomial with Painlevé second parameter transformation.

math-ph↗

arXiv2026

Quantitative analysis and simulation of Noncommutative Langmuir Oscillator solutions

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 for the solution of that equation in noncommutative framework incorporating associated discrete Lax system. Further the standard Darboux transformation on arbitrary eigenfunctions of the Lax system are presented in quasideterminants for few index values. Moreover, these computations include the derivation of noncommutative version of nonabelian discrete nonlinear Schr$\ddot{o}$dinger which coincides with its classical model under commutative limit. The end portion of this article reveals the identity of noncommutative formalism incorporating a derivation of an equation of motion which coincides with its existing commutative form in background zero value of spectral parameter.

nlin.SI↗

arXiv2026

The Quantitative and dynamical analysis of anisotropic dispersive optical solitons

In this article, we explore the integrable aspects of generalized non-linear fluid equation possessing mixed spatial and time evolutions. This non-linear model has been acknowledged as integrable tool for the non-linear dynamical character- ization of dense material such as in optical fibre, metallic ionic fluid. This model widely has been applied in physical interpretations of electromagnetic propaga- tion through perturbed charged plasma. Here, we use few integrable approaches and attain a broad range of solitary solutions involve deep analytical analysis. These results are furnished with computational simulations, which enrich under- standing about the accurate pictorial flow of energy. We also present a bifurcation analysis for canonical coordinates to examine the impact of parameter variations on non-linear behavior of the systems under consideration. Subsequently, we per- form stability analysis to evaluate the robustness of optical solitons features in the vicinity of equilibrium points. These results establish the reliable and accurate framework for analyzing non linear response of materials for energy propagation by varying physical parameters associated with this non-linear equation model.

physics.optics↗

arXiv2026

Stochastic Analysis of Fifth-Order KdV Soliton in Damping Regime and Reduction to Painlevé Second Equation

This work presents a stochastic analysis of fifth-order KdV soliton momentum distribution in a damping regime. An explicit representation of the soliton momentum associated with amplitude variation is derived in terms of a random time function in the presence of dissipation. Statistical interpretations of soliton propagation modes, amplitude fluctuations, and amplification are analyzed within a $δ$-correlated Gaussian random framework. Graphical results obtained using Python illustrate the physical insight into amplitude fluctuation and energy flow. Finally, under a dominant approximation, the nonlinear momentum evolution equation is shown to reduce to the Painlevé second equation, a well-known integrable model appearing in diverse physical systems.

math-ph↗

arXiv2025

Backlund transformation of Kaup Kupershmidt equations with mutli soliton solutions un Darboux framewor

This article encloses the derivation of Darboux solutions for Kaup Kupershmidt equations with their generalization in determinantal form. One of the main focuses of this work is to construct the Backlund transformation for the different solutions of that equation through its associated Riccati equation and then that transformations further reduces to its algebraic analogue with the help of One-fold Darboux solution. Finally, its exact solutions upto three solitons are calculated with their graphical representations which reveal dynamical profiles of these solutions.

nlin.SI↗

arXiv2024

Quantum Painlevé II solution and Approximated analytic solution of the Yukawa Potential

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 form appears as a dominant term of that potential. Further, we show that Painlevé II Riccati solution is an equivalent representation of centrifugal expression of radial Schrödinger potential. This expression is used to derive the approximated form of the Yukawa potential of radial Schrödinger equation which can be solved by applying the Nikiforov-Uvarov method. Finally, we express the approximated form of Yukawa potential explicitly in terms of qunatume Painlevé II solution.

math-ph↗

arXiv2023

Reconstruction of symmteric teleparallel gravity with energy conditions

This research investigates the impact of modified gravity on cosmic scales, focusing on $f(Q)$ cosmology. By applying energy conditions, the study reconstructs various $f(Q)$ models, considering an accelerating Universe, quintessence, and a cosmological constant $Λ$. Using up-to-date observational data, including the Supernova Pantheon sample and cosmic chronometer data, Hubble constants $H_0$ are estimated as $70.37^{+0.84}_{-0.92}$ km/sec/Mpc (from $H(z)$ data) and $70.02^{+0.44}_{-0.25}$ km/sec/Mpc (from pantheon compilation of SN Ia data). The matter energy density parameter ($Ω_{0m}$) is calculated as $0.26^{0.015}_{-0.010}$(OHD) and $0.27^{0.025}_{-0.014}$(SN Ia). Furthermore, as a function of redshift $z$, explicit expressions of $f(Q)$ and the EOS parameter $ω$ are produced, and their graphical analysis describes the late time acceleration of the Universe without the usage of dark energy.

gr-qc↗

arXiv2023

Models of f(Q) gravity with electromagnetic field

There are so many ideas that potentially explain the dark energy phenomenon, current research is focusing on a more in-depth analysis of the potential effects of modified gravity on both local and cosmic scales. In this paper we have investigated some cosmic reconstructions in $f (Q)$ cosmology where $Q$ is the non-metricity corresponding to the evolution background in the Friedmann-Lamatre-Robertson-Walker $(FLRW)$ universe. This allows us to determine how any $FLRW$ cosmology can emerge from a particular $f (Q)$ theory. We employ the reconstruction technique to generate explicit formulations of the $f (Q)$ Lagrangian for several types of matter sources like perfect fluid, dust like fluid, stiff fluid and the binary mixture of two fluids. Furthermore, we computed the field equations and equation of state (EoS) parameter $ω$ for two different reconstructed $f(Q)$ models with the variation of the involved constants, which gives the scenario of accelerating universe, quintessence region and cosmological constant. We also observed that the time dependence of $ω$ admits cosmic acceleration. These new $f(Q)$ gravity inspired models may have an impact on gravitational phenomena at other cosmological scales.

gr-qc↗

arXiv2023

Quantum Painlevé II Lax Pair and Quantum (Matrix) Analogues of Classical Painlevé II equation

In this article, we present a new quantum Painlevé II Lax pair which explicitly involves the Planck constant $ \hbar $ and an arbitrary field variable $v$ so these two objects make this new pair different from Flaschka-Newell Painlevé II Lax pair and that pair appears as particular case of our's pair which consolidates the Painlevé II equation from quantum mechanical point of view. It is shown that the compatibility of quantum Painlevé II Lax pair simultaneously yields a quantum Painlevé II equation and a quantum commutation relation between field variable $v $ and independent variable $z$. We manifest that with the different choices of arbitrary field variable system reduces to its classical version, matrix Painlevé II equation and derivative matrix Painlevé II equation. Further, we construct the gauge equivalence of quantum Painlevé II Lax pair whose compatibility condition gives rise to quantum p34 equation that involves $\hbar $ with power $+1$ which makes our system more quantized as compared to the existed one that carries $\hbar $ with power $+2$.

math-ph↗

arXiv2023

Non-trivial Darboux solutions of Classical Painlevé second equation

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 system of that equation carries similar structure as other integrable systems possess in AKNS scheme. That system yields non-trivial Darboux solutions of classical Painlevé second equation which are further generalized to the $N$-th form in terms of Wranskian. Finally we present the exact solutions of that equation through its associated Riccati system.

math-ph↗

arXiv2023

Darboux Wronskian solutions of Ito typed coupled KdV equation with exact solitonic solutions and conserved densities

In this article, we derive the Darboux solutions of Ito type coupled KdV equation in Darboux framework which is associated with Hirota Satsuma systems. Then we generalise $N$-fold Darboux transformations in terms of Wronskians. We also derive the exact multi-solitonic solutions for the coupled field variables of that system in the background of zero seed solutions. The last section encloses the derivation of continuity equation with several conserved densities through its Riccati equation.

nlin.SI↗

arXiv2017

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

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 $ 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.

math-ph↗

arXiv2014

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

In this paper, I construct the Darboux transformations for the non-commutative Toda solutions at $ n=1 $ with the help of linear systems whose compatibility condition yields zero curvature representation of associated systems of non-linear differential equations. I also derive the quasideterminant solutions of the non-commutative Painlevé II equation by taking the Toda solutions at $ n=1 $ as a seed solution in its Darboux transformations. Further by iteration, I generalize the Darboux transformations of the seed solutions to $ N$-th form. At the end I describe the zero curvature representation of quantum Painlevé II equation that involves Planck constant $ \hbar $ explicitly and system reduces to the classical Painlevé II when $ \hbar \rightarrow 0 $.

math-ph↗

arXiv2012

Lax pair representation and Darboux transformation of NC Painlevé-II equation

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 remarkable aspects of these equations such as Painlevé property, Lax representation, Darboux transformation and their connection to well know integrable equations. This paper is devoted to the Lax formulation, Darboux transformation and Quasideterminant solution of noncommutative Painlevé second equation which is recently introduced by V. Retakh and V. Rubtsov.

math-ph↗