相关论文: Solutions to the ABS lattice equations via general…

We analyze the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization (one linear factor) after 2 steps of…

Nonisospectral integrable systems can describe solitary waves in nonuniform media. In this paper, we apply the Cauchy matrix approach to construct three types of nonisospectral matrix modified Korteweg-de Vries (mKdV) eqautions and present…

Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of…

The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non--abelian theories. Possible applications of these solutions to…

In this work, we provide conditions for nonlinear monotone semigroups on locally convex vector lattices to give rise to a generalized notion of viscosity solutions to a related nonlinear partial differential equation. The semigroup needs to…

In the paper we derive infinitely many conservation laws for the ABS lattice equations from their Lax pairs. These conservation laws can algebraically be expressed by means of some known polynomials. We also show that H1, H2, H3, Q1, Q2, Q3…

The new examples are found of the constraints which link the 1+2-dimensional and multifield integrable equations and lattices. The vector and matrix generalizations of the Nonlinear Schr\"odinger equation and the Ablowitz-Ladik lattice are…

A series of integral lattices parametrised by integers $k,m,n$ are introduced and investigated, where $n$ is the rank of the lattice, including the root lattices described in a uniform way and unimodular lattices such as the Niemeier…

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…

A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…

A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing…

We discuss an algorithm for the approximate solution of Schrodinger's equation for lattice gauge theory, using lattice SU(3) as an example. A basis is generated by repeatedly applying an effective Hamiltonian to a ``starting state.'' The…

In this paper, we first present a unified framework for the modelling of generalized lattice Boltzmann method (GLBM). We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct…

The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper we review the theoretical foundations and the most basic algorithms required to implement a typical lattice…

Lax pairs with operator valued coefficients, which are explicitly connected by means of an additional condition, are considered. This condition is proved to be covariant with respect to the Darboux transformation of a general form.…

We explicitly obtain the $m$-soliton solutions of the (1+2)-dimensional matrix Davey-Stewartson equation from the known general solution of the matrix Toda chain with fixed ends. We write these solutions in terms of $m+m$ independent…

We consider the Cauchy problem to the 3D fractional Schr\"odinger equation with quadratic interaction of $u\bar u$ type. We prove the global existence of solutions and scattering properties for small initial data. For the proof, one novelty…

Quantum systems on a one-dimensional lattice are ubiquitous in the study of models exactly-solved by Bethe Ansatz techniques. Here it is shown that including global-range interaction opens scope for Bethe Ansatz solutions that are not…

Recent progress of lattice QCD study of nuclear forces (potentials) is reviewed. Scattering phase shift is an important observable for two particle system. In lattice QCD, phase shifts are calculated from long distance behavior of…

The method of separation of variables can be used to solve many separable linear partial differential equations (LPDEs). Moreover, variable separation solutions usually are some trigonometric series. In the paper, base on some ideas of this…