Related papers: Liouvillian Propagators, Riccati Equation and Diff…
In this paper, we examine the non-relativistic stationary Schr\"odinger equation from a differential Galois-theoretic perspective. The main algorithmic tools are pullbacks of second order ordinary linear differential operators, so as to…
This thesis is concerning to the Differential Galois Theory point of view of the Supersymmetric Quantum Mechanics. The main object considered here is the non-relativistic stationary Schr\"odinger equation, specially the integrable cases in…
In this paper, we find the quantum propagator for a general time-dependent quadratic Hamiltonian. The method is based on the properties of the propagator and the fact that the quantum propagator fulfills two independent partial differential…
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…
In this paper we develop a differential Galois theory for algebraic Lie-Vessiot systems in algebraic homogeneous spaces. Lie-Vessiot systems are non autonomous vector fields that are linear combinations with time-dependent coefficients of…
In this paper, we argue for the utility of deterministic inference in the classical problem of numerical linear algebra, that of solving a linear system. We show how the Gaussian belief propagation solver, known to work for symmetric…
Here we examine the propagation of relativistic fields in spacetime using the viewpoint applied to derive the Rayleigh--Sommerfeld diffraction integral in three--dimensional space. We use this theory to find the propagators for both the…
We extend Kovacic's algorithm to compute the differential Galois group of some second order parameterized linear differential equation. In the case where no Liouvillian solutions could be found, we give a necessary and sufficient condition…
Differential Galois theory has played important roles in the theory of integrability of linear differential equation. In this paper we will extend the theory to nonlinear case and study the integrability of the first order nonlinear…
A new parametrisation of the Eilenberger equations of superconductivity in terms of the solutions to a scalar differential equation of the Riccati type is introduced. It is shown that the quasiclassical propagator, and in particular the…
We study a Sturm-Liouville type eigenvalue problem for second-order differential equations on the infinite interval. Here the eigenfunctions are nonzero solutions exponentially decaying at infinity. We prove that at any discrete eigenvalue…
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
This work is concerned with the study of explicit solutions for generalized coupled reaction-diffusion and Burgers-type systems with variable coefficients. Including nonlinear models with variable coefficients such as diffusive…
A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
We apply Kovacic's algorithm from differential Galois theory to show that all complex non-oscillatory solutions (finite exponential of convergence of zeros) of certain Hill equations considered by Bank and Laine using Nevanlinna theory must…
The aim of this paper is to give a new result of the differential Galois theory of linear ordinary differential equations. In particular, we compute differential Galois group for special type non-resonant Fuchsian system.
This paper is an overview of our works which are related to investigations of the integrability of natural Hamiltonian systems with homogeneous potentials and Newton's equations with homogeneous velocity independent forces. The two types of…
We study first-order ordinary differential equations such that the intrinsic Gauss curvature of the associated surface depends only on the independent variable: $\mathcal{K}(x,u)=\kappa(x)$, showing that this geometrically motivated class…
We point out the relevance of the Differential Galois Theory of linear differential equations for the exact semiclassical computations in path integrals in quantum mechanics. The main tool will be a necessary condition for complete…