Related papers: Discrete Integrable Equations over Finite Fields
We present a simple proof of the well-known fact concerning the number of solutions of diagonal equations over finite fields. In a similar manner, we give an alternative proof of the recent result on generalizations of Carlitz equations. In…
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the $\tau$ function are presented. B\"acklund transformations of the…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to…
A symmetry reduction of the Dirac equation is shown to yield the system of ordinary differential equations whose integrability by quadratures is closely connected to the stationary mKdV hierarchy.
This paper investigates the well posedness of ordinary differential equations and more precisely the existence (or uniqueness) of a flow through explicit compactness estimates. Instead of assuming a bounded divergence condition on the…
We have proposed, in our previous papers, a method to characterize integrable discrete soliton equations. In this paper we generalize the method further and obtain a $q$-difference Toda equation, from which we can derive various…
By the theory of pseudoinverse matrices and orthoprojectors, we establish a criterion for the solvability and find the general form of solutions of an integrodifferential equation with with impulse action and control. The general form of…
The hierarchy of commuting maps related to a set-theoretical solution of the quantum Yang-Baxter equation (Yang-Baxter map) is introduced. They can be considered as dynamical analogues of the monodromy and/or transfer-matrices. The general…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
Involutive non-degenerate set theoretic solutions of the Yang-Baxter equation are considered, with a focus on finite solutions. A rich class of indecomposable and irretractable solutions is determined and necessary and sufficient conditions…
We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
We present a general purpose method for solving partial differential equations on a closed surface, based on a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang [J. Comput. Phys. 252 (2013), pp. 606-624]…
We construct integrable modifications of 2d lattice gauge theories with finite gauge groups.
We investigate discretizations of the integrable discrete nonlinear Schr\"odinger dynamical system and related symplectic structures. We develop an effective scheme of invariant reducing the corresponding infinite system of ordinary…
We are concerned with the Cauchy problem for the KdV equation for nonsmooth locally integrable initial profiles q's which are, in a certain sense, essentially bounded from below and q(x)=O(e^{-cx^{{\epsilon}}}),x\rightarrow+\infty, with…
In this paper, we present and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then present a specific version of Cramer's rule…
Superconformal indices of 3d N=2 supersymmetric field theories are investigated from the Yang-Baxter equation point of view. Solutions of the star-triangle relation, vertex and IRF Yang-Baxter equations are expressed in terms of the…
Hirota's discrete Korteweg-de Vries equation (dKdV) is an integrable partial difference equation on 2-dimensional integer lattice, which approaches the Korteweg-de Vries equation in a continuum limit. We find new transformations to other…
Systems of integration-by-parts identities play an important role in simplifying the higher-loop Feynman integrals that arise in quantum field theory. Solving these systems is equivalent to reducing integrals containing numerator products…