A geometric realization of the periodic discrete Toda lattice and its tropicalization

Commuting Time Evolutions in the Tropical Periodic Toda Lattice

The tropical (ultradiscrete) periodic Toda lattice is a dynamical system derived from a time-discretized version of the periodic Toda lattice through a limiting procedure called tropicalization. We propose a new formulation for this dynamical system with a representation by two-colored strips. Based on this formulation, a family of its commuting time evolutions is constructed.

散射结构的无散Toda τ函数混合Hessian

Spectral Structure of the Mixed Hessian of the Dispersionless Toda $τ$-Function

研究无散Toda τ函数的混合Hessian，探讨其谱结构及在固定希尔伯特空间中的权重对称块实现在分析阈值处的谱转变。

A geometric realization of the ultradiscrete periodic Toda lattice via tropical plane curves

This is a review article on a tropical geometric realization of the ultradiscrete periodic Toda lattice (UD-pTL). Time evolution of the UD-pTL is translated into an addition on the Picard group of its spectral curve, which is a tropical hyperelliptic curve of arbitrary genus depending on the system size. The addition on the Picard group can be realized by using intersection of several tropical plane curves, one of which is the spectral curve. In addition, the tropical eigenvector map, which maps a point in the phase space of the UD-pTL into a set of points on the spectral curve, can also be re…

Discrete time Toda systems

In this paper, we discuss several concepts of the modern theory of discrete integrable systems, including: - Time discretization based on the notion of Bäcklund transformation; - Symplectic realizations of multi-Hamiltonian structures; - Interrelations between discrete 1D systems and lattice 2D systems; - Multi-dimensional consistency as integrability of discrete systems; - Interrelations between integrable systems of quad-equations and integrable systems of Laplace type; - Pluri-Lagrangian structure as integrability of discrete variational systems. All these concepts are illustrated by the di…

The affine $A_{n-1}^{(1)}$ Toda fields with boundary reflection

We study the affine $A_{n-1}^{(1)}$ Toda fields with boundary reflection. Our approach is based on the free field approach. We construct free field realizations of the boundary state and its dual. For an application of these realizations, we present integral representations for the form factors of the local operators. In a limiting case $ρ\to \infty$, our integral representations reproduce those of form factors for the SU(n) invariant massive Thirring model with boundary reflection [nlin.SI/0010020,Int.J.Mod.Phys.A16,no.15 (2001)2665-2689].

修正的开放Toda链与准可积性

Modified open Toda chain and quasi-integrability

本文研究了通过引入三体相互作用项修正的开放Toda链，展示了其准可积性特征及守恒量的长期存在。