arXiv subjects

Anindya Ghose-Choudhury

Publications and source records attributed to Anindya Ghose-Choudhury.

3 recordsLinked to original sources

arXiv2026

Generalized quantum theory for accessing nonlinear systems: the case of Liénard and Levinson-Smith equations

We show that a recently introduced generalized scheme of quantum mechanics has connections to Liénard and Levinson-Smith classes of nonlinear systems. For the Liénard type, which has coefficients of odd and odd symmetry, we demonstrate that closed form solutions exist on conversion to the Abel form. For the Levinson-Smith equations, we find their relevance to position-dependent mass systems, with an interesting off-shoot that solitonic-like solutions emerge from the condition of the level surface in the system.

quant-ph↗

arXiv2025

On novel Hamiltonian descriptions of some three-dimensional non-conservative systems

We present novel Hamiltonian descriptions of some three-dimensional systems including two well-known systems describing the three-wave-interaction problem and some well-known chaotic systems, namely, the Chen, Lü, and Qi systems. We show that all of these systems can be described in a Hamiltonian framework in which the Poisson matrix $\mathcal{J}$ is supplemented by a resistance matrix $\mathcal{R}$. While such resistive-Hamiltonian systems are manifestly non-conservative, we construct higher-degree Poisson matrices via the Jordan product as $\mathcal{N} = \mathcal{J} \mathcal{R} + \mathcal{R} \mathcal{J}$, thereby leading to new bi-Hamiltonian systems. Finally, we discuss conformal Hamiltonian dynamics on Poisson manifolds and demonstrate that by appropriately choosing the underlying parameters, the reduced three-wave-interaction model as well as the Chen and Lü systems can be described in this manner where the concomitant non-conservative part of the dynamics is described with the aid of the Euler vector field.

math-ph↗

arXiv2019

Reduction and Hamiltonian aspects of a model for virus-tumour interaction in oncolytic virotherapy

We analyse the Hamiltonian structure of a system of first-order ordinary differential equations used for modeling the interaction of an oncolytic virus with a tumour cell population. The analysis is based on the existence of a Jacobi Last Multiplier for the system and a time dependent first integral. For suitable conditions on the model parameters this allows for the reduction of the problem to a planar system of equations for which the time dependent Hamiltonian flows are described. The geometry of the Hamiltonian flows are finally investigated using the symplectic and cosymplectic methods.

q-bio.PE↗