相关论文: An implementation of the polynomial Lie algebra me…
A general way to construct ladder models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. It is shown that corresponding to these SU(2) symmetric…
In this paper we present an algebraic study concerning the general second order linear differential equation with polynomial coefficients. By means of Kovacic's algorithm and asymptotic iteration method we find a degree independent…
We implement two algorithms in MATHEMATICA for classifying automorphisms of lower-dimensional non-commutative Lie algebras. The first algorithm is a brute-force approach whereas the second is an evolutionary strategy. These algorithms are…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of diagonalization of these operators…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine…
The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose…
In many applications, one encounters signals that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are examples of ubiquitous mathematical objects that have a non Euclidean structure. The application of…
We consider a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, derive general scaling equation for the model, and analyse the connection between its particular forms…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
In the article, two implementations of the representation of the complex Lie algebra $\mathfrak{sl}_2$ on the algebra of symmetric polynomials $\Lambda_n$ by differential operators are proposed. The realizations of irreducible…
Many important systems across biology, engineering, physics, and economics are characterized by polynomial ordinary differential equations (ODEs), yet analytical solutions are rare. We develop a framework for identifying and solving a broad…
A new procedure for the construction of higher-dimensional Lie-Hamilton systems is proposed. This method is based on techniques belonging to the representation theory of Lie algebras and their realization by vector fields. The notion of…
A class of non-Hermitian quadratic su(2) Hamiltonians having an anti-linear symmetry is constructed. This is achieved by analysing the possible symmetries of such systems in terms of automorphisms of the algebra. In fact, different…