Related papers: Prototype and reduced nonlinear integrable lattice…
This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in…
Several integrable semi-discretizations are known in the literature for the massive Thirring system in characteristic coordinates. We present for the first time an integrable semi-discretization of the massive Thirring system in laboratory…
In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. In this paper we construct other examples of integrable dynamics of Toda-type on the square lattice, as well as on the triangular lattice,…
We have undertaken an algorithmic search for new integrable semi-discretizations of physically relevant nonlinear partial differential equations. The search is performed by using a compatibility condition for the discrete Lax operators and…
Numerical modelling of several coupled passive linear dynamical systems (LDS) is considered. Since such component systems may arise from partial differential equations, transfer function descriptions, lumped systems, measurement data, etc.,…
We establish the pluri-Lagrangian structure for families of B\"acklund transformations of relativistic Toda-type systems. The key idea is a novel embedding of these discrete-time (one-dimensional) systems into certain two-dimensional…
This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable…
We present a study of a quasi-integrable deformation of the three-particle open Toda chain, constructed by introducing a translation-invariant three-body interaction terms. Although this modification explicitly breaks the exact…
An overview is given of basic models combining discreteness in their linear parts (i.e. the models are built as dynamical lattices) and nonlinearity acting at sites of the lattices or between the sites. The considered systems include the…
A fairly complete list of Toda-like integrable lattice systems, both in the continuous and discrete time, is given. For each system the Newtonian, Lagrangian and Hamiltonian formulations are presented, as well as the 2x2 Lax representation…
This paper presents a modular framework for motion planning using movement primitives. Central to the approach is Contraction Theory, a modular stability tool for nonlinear dynamical systems. The approach extends prior methods by achieving…
Given a dynamical system with $m$ independent conserved quantities, we construct a multi-parameter family of new systems in which these quantities evolve monotonically and proportionally, and are replaced by $m-1$ conserved linear…
Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix…
Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete…
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…
Some new developments in constrained Lax integrable systems and their applications to physics are reviewed. After summarizing the tau function construction of the KP hierarchy and the basic concepts of the symmetry of nonlinear equations,…
A discrete theory for implicit nonholonomic Lagrangian systems undergoing elastic collisions is developed. It is based on the discrete Lagrange-d'Alembert-Pontryagin variational principle and the dynamical equations thus obtained are the…
We propose a lattice Boltzmann color-gradient model for immiscible ternary fluid flows, which is applicable to the fluids with a full range of interfacial tensions, especially in near-critical and critical states. An interfacial force for…
A coupled bosonic massive Thirring model (BMTM), involving an interaction between the two independent spinors, is introduced and shown to be integrable. By incorporating suitable reductions between the field components of the coupled BMTM,…