相关论文: 2D Toda Chain, Commuting Difference Operators and …
We study the Riemann-Hilbert problem associated to flat sections of oper connections of arbitrary rank on the twice-punctured Riemann sphere with irregular singularities of the mildest type. We construct the solutions in terms of the…
A general Casoratian formulation is proposed for the 2D Toda lattice equation, which involves coupled eigenfunction systems. Various Casoratian type solutions are generated, through solving the resulting linear conditions and using a…
It is shown how to study the 2-D Toda system for SU(n+1) using Nevanlinna theory of meromorphic functions and holomorphic curves. The results generalize recent results of Jost - Wang and Chen - Li.
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…
We develop a holomorphic equivalence between on one hand the space of pairs (stable bundle, flat connection on the bundle) and the "sheaf of holomorphic connections" (the sheaf of splittings of the one-jet sequence) for the determinant…
We apply the Separation of Variables method to obtain eigenvectors of commuting Hamiltonians in the quantum relativistic Toda chain at a root of unity with boundary interaction.
The relation between the Darboux transformation and the solutions of the full Kostant Toda lattice is analyzed. The discrete Korteweg de Vries equation is used to obtain such solutions and the main result of [1] is extended to the case of…
We give a combinatorial criterion for the tangent bundle on a smooth toric variety to be stable with respect to a given polarisation in terms of the corresponding lattice polytope. Furthermore, we show that for a smooth toric surface and a…
We prove separation of variables for the most general (Dn type) periodic Toda lattice with 2x2 Lax matrix. It is achieved by finding proper normalisation for the corresponding Baker-Akhiezer function. Separation of variables for all other…
An alternative derivation of the known action-angle map of the standard open Toda lattice is presented based on its identification as the natural map between two gauge slices in the relevant symplectic reduction of the cotangent bundle of…
By encoding configurations of the ultra-discrete Toda lattice by piecewise linear paths whose gradient alternates between $-1$ and $1$, we show that the dynamics of the system can be described in terms of a shifted version of Pitman's…
Originally a model for wave propagation on the line, the Toda lattice is a wonderful case study in mechanics and symplectic geometry. In Flaschka's variables, it becomes an evolution given by a Lax pair on the vector space of real,…
In this paper, we have studied the kink and antikink solutions in several neutral scalar models in 1+1 dimension. We follow the standard approach to write down the leading order and the second order force between long distance separated…
Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant…
The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated to an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov--Shabat equations are…
Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping,…
We discuss the bihamiltonian geometry of the Toda lattice (periodic and open). Using some recent results on the separation of variables for bihamiltonian manifolds, we show that these systems can be explicitly integrated via the classical…
This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations,…
By applying the Hamiltonian reduction method to the cotangent bundle over loop groups we recover the well-known classical trigonometric $r$-matrices of the periodic Toda lattice.
We introduce a criterion that a given bihamiltonian structure allows a local coordinate system where both brackets have constant coefficients. This criterion is applied to the bihamiltonian open Toda lattice in a generic point, which is…