Related papers: Obtaining eigenvalues and solutions for a class of…
A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using a gauging of…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, allowing a unified treatment of a large body of polynomial…
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra,…
This work provides a method(an algorithm) for solving the solvable unary algebraic equation $f(x)=0$ ($f(x)\in\mathbb{Q}[x]$) of arbitrary degree and obtaining the exact radical roots. This method requires that we know the Galois group as…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…
We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these…
We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…
We consider the problem of finding the spectrum of an operator taking the form of a low-rank (rank one or two) non-normal perturbation of a well-understood operator, motivated by a number of problems of applied interest which take this…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
The problem of group classification of one class of quasilinear equations of hyperbolic type with two independent variables has been solved completely.
In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are…
In this preliminary work, we present nonstandard time-stepping strategies to solve differential equations based on the algebraic estimation method applied to the estimation of time-derivative, which provides interesting properties of…
The eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces of arbitrary dimension are computed by separating variables in geodesic polar coordinates. These eigenfunctions are used to derive the heat kernel of the…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
I revisit the so called "bispectral problem" introduced in a joint paper with Hans Duistermaat a long time ago, allowing now for the differential operators to have matrix coefficients and for the eigenfunctions, and one of the eigenvalues,…