English
Related papers

Related papers: Toda Lattice Models with Boundary

200 papers

Using U_q(a_n^(1))- and U_q(a_2n^(2))-invariant R-matrices we construct exact S-matrices in two-dimensional space-time. These are conjectured to describe the scattering of solitons in affine Toda field theories. In order to find the…

High Energy Physics - Theory · Physics 2009-10-30 G. M. Gandenberger

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…

solv-int · Physics 2008-02-03 Yuri B. Suris

In Part I [arXiv:0902.4873 [nlin.SI]] soliton solutions to the ABS list of multi-dimensionally consistent difference equations (except Q4) were derived using connection between the Q3 equation and the NQC equations, and then by reductions.…

Exactly Solvable and Integrable Systems · Physics 2011-05-27 Jarmo Hietarinta , Da-jun Zhang

We use representation theory to construct integral formulas for solutions to the quantum Toda lattice in general type. This result generalizes work of Givental for SL(n)/B in a uniform way to arbitrary type and can be interpreted as a kind…

Representation Theory · Mathematics 2011-03-29 Konstanze Rietsch

We find new solutions, including soliton-like ones, for a special case of non-Abelian loop Toda equations associated with complex general linear groups. We use the method of rational dressing based on an appropriate block-matrix…

Mathematical Physics · Physics 2009-06-22 Kh. S. Nirov , A. V. Razumov

For the 1+1 dimensional Lax pair with a symplectic symmetry and cyclic symmetries, it is shown that there is a natural finite dimensional Hamiltonian system related to it by presenting a unified Lax matrix. The Liouville integrability of…

Exactly Solvable and Integrable Systems · Physics 2015-05-28 Zi-Xiang Zhou

In this paper, we study the solutions of Toda systems on Riemann surface in the critical case, we prove a sufficient condition for the existence of solutions of Toda systems.

Analysis of PDEs · Mathematics 2007-05-23 Jiayu Li , Yuxiang Li

We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an…

Numerical Analysis · Mathematics 2025-01-22 Oliver Boolakee , Martin Geier , Laura De Lorenzis

We consider a Toda system of Liouville equations defined on a compact surface which arises as a model for non-abelian Chern-Simons vortices. For the first time the range of parameters $\rho_1 \in (4k\pi , 4(k+1)\pi)$, $k \in \mathbb{N}$,…

Analysis of PDEs · Mathematics 2017-01-25 Aleks Jevnikar , Sadok Kallel , Andrea Malchiodi

We study a simple nonlinear model defined on the cubic lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the…

Exactly Solvable and Integrable Systems · Physics 2017-12-08 V. E. Vekslerchik

We propose a new multi-component two-dimensional Toda lattice hierarchy (mc2dTLH) which includes two-dimensional Toda lattice equation with self-consistent sources (2dTLSCS) as the first non-trivial equation. The Lax representations for…

Exactly Solvable and Integrable Systems · Physics 2009-11-13 Xiaojun Liu , Yunbo Zeng , Runliang Lin

We establish unique continuation for various discrete nonlinear wave equations. For example, we show that if two solutions of the Toda lattice coincide for one lattice point in some arbitrarily small time interval, then they coincide…

Exactly Solvable and Integrable Systems · Physics 2012-04-03 Helge Krueger , Gerald Teschl

We develop the idea that a natural link between Boltzmann schemes and finite volumes exists naturally: the conserved mass and momentum during the collision phase of the Boltzmann scheme induces general expressions for mass and momentum…

Cellular Automata and Lattice Gases · Physics 2023-06-28 François Dubois , Pierre Lallemand

Bi-Hamiltonian structure and Lax pair formulation with the spectral parameter of the generalized fermionic Toda lattice hierarchy as well as its bosonic and fermionic symmetries for different (including periodic) boundary conditions are…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 V. V. Gribanov , V. G. Kadyshevsky , A. S. Sorin

We discuss some properties of the soliton equations of the type, partial derivative u/partial derivative t = S [u, (u) over bar], where S is a nonlinear operator differential in x, and present the additivity theorems of the class of the…

Mathematical Physics · Physics 2014-03-17 Jian-Jun Shu

The subject of this paper is a connection between d-orthogonal polynomials and the Toda lattice hierarchy. In more details we consider some polynomial systems similar to Hermite polynomials, but satisfying $d+2$-term recurrence relation, $d…

Mathematical Physics · Physics 2019-04-18 Emil Horozov

In this paper we define a family of systems which have similarities with the Toda lattice. We construct two Lax pair representations and the associate Poisson structures for these systems. These systems lie between the classical Toda…

Mathematical Physics · Physics 2015-04-29 Charalampos A. Evripidou

In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories…

High Energy Physics - Phenomenology · Physics 2007-05-23 Abhijit Gadde , Narendra Sahu , Urjit A. Yajnik

A series of new soliton solutions are presented for the inhomogeneous variable coefficient Hirota equation by using the Riemann Hilbert method and transformation relationship. First, through a standard dressing procedure, the N-soliton…

Exactly Solvable and Integrable Systems · Physics 2023-03-01 Huijuan Zhou , Yong Chen

High rank solutions to the 2D Toda Lattice System are constructed simultaneously with the effective calculation of coefficients of the high rank commuting ordinary difference operators. Our technic is based on the study of discrete dynamics…

Mathematical Physics · Physics 2015-06-26 I. M. Krichever , S. P. Novikov