Related papers: Partial differential equations from integrable ver…
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.…
An approach to master symmetries of lattice equations is proposed by the use of discrete zero curvature equation. Its key is to generate non-isospectral flows from the discrete spectral problem associated with a given lattice equation. A…
In this paper we develop a way of obtaining Green's functions for partial differential equations with linear involutions by reducing the equation to a higher-order PDE without involutions. The developed theory is applied to a model of heat…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in…
This paper explores the embedding of lattice structures $L \subseteq \mathbb{R}^n$ into smooth manifolds $M \subseteq \mathbb{R}^n$ through a rigorous mathematical framework. Building upon the foundational results established in "Embedding…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that…
Applying a unifying Lax operator approach to statistical systems a new class of integrable vertex models based on quantum algebra is proposed, which exhibits a rich variety for generic q, q roots of unity and q -> 1. Exact solutions are…
With the aim of exploring a massive model corresponding to the perturbation of the conformal model [hep-th/0211094] the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is…
We use Vessiot theory and exterior calculus to solve partial differential equations(PDEs) of the type uyy = F(x, y,u,ux,uy,uxx,uxy) and associated evolution equations. These equations are represented by the Vessiot distribution of vector…
We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…
The partition function of the six-vertex model on a square lattice with domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix model or a discretized version of it (similar to sums over Young diagrams), depending on…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…
We apply the algebraic Bethe ansatz developed in our previous paper \cite{CM} to three different families of U(1) integrable vertex models with arbitrary $N$ bond states. These statistical mechanics systems are based on the higher spin…
Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…
We develop a theory of the Cauchy problem for linear evolution systems of partial differential equations with the Caputo-Dzrbashyan fractional derivative in the time variable $t$. The class of systems considered in the paper is a fractional…
Fractional spectral collocation (FSC) method based on fractional Lagrange interpolation has recently been proposed to solve fractional differential equations. Numerical experiments show that the linear systems in FSC become extremely…
We obtain solution representation formulas for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified transform method (UTM), also known as the Fokas method. We first…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…