Related papers: Classification of Toda-type tt*-structures and $\m…
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…
Based on the work of Guillarmou, Kupiainen, and Rhodes, we construct compactified imaginary Toda theory on closed Riemann surfaces, extending the rank-one construction to the higher-rank setting. This theory is expected to describe critical…
It is shown that the Affine Toda models (AT) constitute a ``gauge fixed'' version of the Conformal Affine Toda model (CAT). This result enables one to map every solution of the AT models into an infinite number of solutions of the…
In this paper, we consider the following elliptic Toda system associated to a general simple Lie algebra with multiple singular sources \begin{equation*} \begin{cases} -\Delta…
Generalizations of GL(n) abelian Toda and $\widetilde{GL}(n)$ abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by…
We reformulate the singularity confinement of the discrete Toda equation. We prove the co-primeness property, which has been introduced in our previous paper (arXiv:1311.0060) as one of the integrability criteria, for the discrete Toda…
We consider the soliton solutions in 1- and (1+1)-dimensional Toda lattice models with a boundary. We make use of the solutions already known on a full line by means of the Hirota's method. We explicitly construct the solutions satisfying…
This paper is the second part of our study on the Toda equations and the cyclic Higgs bundles associated to $r$-differentials over non-compact Riemann surfaces. We classify all the solutions up to boundedness around the isolated singularity…
We construct a new class of positive solutions for a classical semilinear elliptic problem in the plane which arise for instance as the standing-wave problem for the standard nonlinear Schr\"odinger equation or in nonlinear models in…
We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…
The general solution of the two-dimensional integrable generalization of the f-Toda chain with fixed ends is explicitly presented in terms of matrix elements of various fundamental representations of the SL(n|n-1) supergroup. The dominant…
In this paper, we construct a new even constrained B(C) type Toda hierarchy and derive its B(C) type Block type additional symmetry. Also we generalize the B(C) type Toda hierarchy to the $N$-component B(C) type Toda hierarchy which is…
There are two-dimensional Toda field equations corresponding to each (finite or affine) Lie algebra. The question addressed in this note is whether there exist integrable discrete versions of these. It is shown that for certain algebras…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third…
We study some static multi-soliton configurations in the su(N + 1) Toda models. Such configurations exist for N > 1. We construct explicitly a multi-soliton solution for any N and study conditions for having such solutions. The number of…
Let X be an irreducible smooth complex projective curve of genus g>2, and let x be a fixed point. A framed bundle is a pair (E,\phi), where E is a vector bundle over X, of rank r and degree d, and \phi:E_x\to C^r is a non-zero homomorphism.…
We provide a general definition of Toda brackets in a pointed model categories, show how they serve as obstructions to rectification, and explain their relation to the classical stable operations.
We introduce a class of recursions defined over the $d$-dimensional integer lattice. The discrete equations we study are interpreted as higher dimensional extensions to the discrete Toda lattice equation. We shall prove that the equations…
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,…
A direct connection between two sequences of points, one of which is generated by seed mutations in the cluster algebra of type $A^{(1)}_1$ and the other by time evolutions of the periodic discrete Toda lattice, is explicitly given. In this…