Related papers: An Explicit Characterization of Calogero--Moser Sy…

Affine analogues of the Q-functions are constructed using folded instantons partition functions. They are shown to be the solutions of the quantum spectral curve of the N-body elliptic Calogero-Moser (eCM) system, the quantum Krichever…

This is the first in a series of papers in which we describe explicit structural properties of spaces of diagonal rectangular harmonic polynomials in $k$ sets of $n$ variables, both as $GL_k$-modules and $S_n$-modules, as well as some of…

We consider two elliptic coupled systems of relevance in the fluid dynamics. These systems are posed on the whole three-dimensional space and they consider the action of external forces. The first system deals with the simplified…

We study the problem of how the Floquet property manifests for periodic Schr\"{o}dinger operators which are known to have multiple of asymptotic spectral solutions. The main conclusions are made for elliptic potentials, we demonstrate that…

This is both an expository and research paper where we advocate a systematic study of continuous analogues of finite partially ordered sets, convex polytopes, oriented matroids, arrangements of subspaces, finite simplicial complexes, and…

In this paper we define a rigid rational homotopy type, associated to any variety $X$ over a perfect field $k$ of positive characteristic. We prove comparison theorems with previous definitions in the smooth and proper, and log-smooth and…

Taking the coupled KdV system as a simple example, analytical and nonsingular complexiton solutions are firstly discovered in this letter for integrable systems. Additionally, the analytical and nonsingular positon-negaton interaction…

In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamiltonians have represented free motion, but here we consider the…

Coupled triple well (phi6) one-dimensional potentials occur in both condensed matter physics and field theory. Here we provide a set of exact periodic solutions in terms of elliptic functions (domain wall arrays) and obtain single domain…

We study a class of logarithmic Schrodinger equations with periodic potential which come from physically relevant situations and obtain the existence of infinitely many geometrically distinct solutions.

There is a lack of knowledge about the topological invariants of non-linear $d$-dimensional systems with a periodic potential. We study these systems through a classification of the linearized NLS/GP equation around their soliton solutions.…

We study existence of helical solitons in the vector modified Korteweg-de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems,…

Calogero-Moser models can be generalised for all of the finite reflection groups. These include models based on non-crystallographic root systems, that is the root systems of the finite reflection groups, H_3, H_4, and the dihedral group…

We obtain the full hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated hamiltonian functionals and the corresponding Poisson structures follow from…

We carry out a Kovalevskaya analysis of the Riccati hierarchy. We determine all indicial loci and Kovalevskaya exponents and identify a rigid recursive structure governing how free parameters enter Laurent solutions. We further identify a…

In the framework of Clifford analysis, a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space $\mR^{m+1}$, including a higher dimensional generalization of the complex logarithmic function. Their…

Let $d$ be a positive integer, $\mathbb K$ an algebraically closed field of characteristic 0 and $ X$ an elliptic curve defined over K. We study the hyperelliptic curves equipped with a projection over $ X$, such that the natural image of $…

For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarizations on the strata and the behaviour of the polarizations…

We investigate the linearized KdV equation on a metric tree consisting of three different types of bonds: incoming unbounded root, two finite bonds, and four outgoing unbounded bonds. Under natural assumptions at the vertices, we obtain the…

The theory of representations of quivers and of their preprojective algebras are reviewed. In particular, moduli spaces of representations of these algebras, quiver varieties and reflection functor are described. The proof that the…