Related papers: Integrable 1D Toda cellular automata
We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy…
We construct $(D-3)$-brane and instanton solutions using $N \le 10-D$ one-form field strengths in $D$ dimensions, and show that the equations of motion can be cast into the form of the $SL(N+1,R)$ Toda equations. For generic values of the…
In this work we study the electromagnetic field at Finite Temperature via the massless DKP formalism. The constraint analysis is performed and the partition function for the theory is constructed and computed. When it is specialized to the…
We present a simplified model consisting on two linear elliptic boundary-value problems that represent a single step and single fixed-point iteration in an electrochemical battery model. The main variables are the concentration and the…
We are studying Runge-Kutta methods along complex paths of integration from a geometric point of view. Thereby we derive special complex time grids, which applied to the problem of integrating a linear autonomous system of ordinary…
We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two…
A method to solve the static field equation of the Faddeev model is presented. For an special combination of the concerned field, we adopt a form which is compatible with the field equation and involves two arbitrary complex functions. As a…
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…
A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is…
We describe an algorithm for computing the convex hull of a finite collection of points in the affine building of SL_d(K), for K a field with discrete valuation. These convex hulls describe the relations among a finite collection of…
Let $k$ be a finite field extension of the function field $\bfF_p(T)$ and $\bar{k}$ its algebraic closure. We count points in projective space $\Bbb P ^{n-1}(\bar{k})$ with given height and of fixed degree $d$ over the field $k$. If…
The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary…
Based on the work of Guillarmou, Kupiainen, and Rhodes, we construct compactified imaginary Toda theory on closed Riemann surfaces, extending the rank-one construction to the higher-rank setting. This theory is expected to describe critical…
We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse…
The aim of this paper is to construct and analyze explicit exponential Runge-Kutta methods for the temporal discretization of linear and semilinear integro-differential equations. By expanding the errors of the numerical method in terms of…
Elasticity property (i.e. no-particle creation) is used in the tree level scattering of scalar particles in 1+1 dimensions to construct the affine Toda field theory(ATFT) associated with root systems of groups $a_2^{(2)}$ and $c_2^{(1)}$. A…
We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in this respect, namely quad-graphs, the cellular…
We present a method of incorporating the discrete dipole approximation (DDA) method with the point matching method to formulate the T-matrix for modeling arbitrarily shaped micro-sized objects. The \emph{T}-matrix elements are calculated…
We show that there exists an alternative procedure in order to extract differential hierarchies, such as the KdV hierarchy, from one--matrix models, without taking a continuum limit. To prove this we introduce the Toda lattice and…
The mathematical P2D model is a system of strongly coupled nonlinear parabolic-elliptic equations that describes the electrodynamics of lithium-ion batteries. In this paper, we present the numerical analysis of a finite element-implicit…