Related papers: Integrable Dispersive Chains and Their Multi-Phase…
A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with $A_n$ symmetry and…
Complete integrability and multisoliton solutions are discussed for a multicomponent Ablowitz-Ladik system with branched dispersion relation. It is also shown that starting from a "diagonal" (in two-dimensions) completely integrable…
We develop a general distributed implementation of an adaptive fast multipole method in three space dimensions. We rely on a balanced type of adaptive space discretisation which supports a highly transparent and fully distributed…
B.A. Dubrovin proved that remarkable WDVV associativity equations are integrable systems. In a simplest nontrivial three-component case these equations can be written as a nondiagonalizable hydrodynamic type system equivalent to a symmetric…
The KP equation has a large family of quasiperiodic multiphase solutions. These solutions can be expressed in terms of Riemann-theta functions. In this paper, a finite-dimensional canonical Hamiltonian system depending on a finite number of…
We address the question of global in time existence of solutions to a magnetoviscoelastic system with general initial data. We show that the notion of dissipative solutions allows to prove such an existence in two and three dimensions. This…
A numerical procedure was developed for solving equations for compressible granular multiphase flows in which the particle volume fraction can range dynamically from very dilute to very dense. The procedure uses a low-dissipation and…
On Bakhvalov-type mesh, uniform convergence analysis of finite element method for a 2-D singularly perturbed convection-diffusion problem with exponential layers is still an open problem. Previous attempts have been unsuccessful. The…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…
Interval Markov decision processes (IMDPs) generalise classical MDPs by having interval-valued transition probabilities. They provide a powerful modelling tool for probabilistic systems with an additional variation or uncertainty that…
The conditions of multi-phase equilibrium are solved for generic polydisperse systems. The case of multiple polydispersity is treated, where several properties (e.g. size, charge, shape) simultaneously vary from one particle to another. By…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
We present doubly-periodic solutions of the infinitely extended nonlinear Schrodinger equation with an arbitrary number of higher-order terms and corresponding free real parameters. Solutions have one additional free variable parameter that…
We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a…
We construct a point transformation between two integrable systems, the multi-component Harry Dym equation and the multi-component extended Harry Dym equation, that does not preserve the class of multi-phase solutions. As a consequence we…
We propose an experimental scheme to effectively assemble chains of dipolar gases with an uniform length in a multi-layer system. The obtained dipolar chains can form a chain crystal with the system temperature easily controlled by the…
The PMCHWT integral equation enables the modelling of scattering of time-harmonic fields by penetrable, piecewise homogeneous, systems. They have been generalised to include the modelling of composite systems that may contain junctions,…
This paper presents two new approaches to decomposing and solving large Markov decision problems (MDPs), a partial decoupling method and a complete decoupling method. In these approaches, a large, stochastic decision problem is divided into…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…