Related papers: Sur un syst\`eme int\'egrable \`a bord
We construct integrable Hamiltonian systems on $G/K$, where $G$ is a quasitriangular Poisson Lie group and $K$ is a Lie subgroup arising as the fixed point set of a group automorphism $\sigma$ of $G$ satisfying the classical reflection…
Bott periodicity for the unitary, orthogonal and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic K-groups with finite coefficients similar periodicity results are…
We compute the genus of a rational quadratic form in terms of the K-theory of a C*-algebra attached to the adelic orthogonal group of the form. As a corollary, one gets a higher composition law for the rational quadratic forms. As an…
We focus on the tranformation matrices between the standard Young-Yamanouchi basis of an irreducible representation for the symmetric group S_n and the split basis adapted to the direct product subgroups S_{n_1} \times S_{n-n_1} . We…
A scheme stemming from the use of pseudospectral approximations to spatial derivatives followed by a time integrator based on trigonometric polynomials is proposed for the numerical solutions of the coupled nonlinear Klein--Gordon…
In this paper, we examine some basic properties of the multiple-Sine-Gordon (MSG) systems, which constitute a generalization of the celebrated sine-Gordon (SG) system. We start by showing how MSG systems can be viewed as a general class of…
In the preceding paper, we derived Coulomb-gas and sine-Gordon Hamiltonians to describe the Kosterlitz-Thouless transition on a fluctuating surface. These Hamiltonians contain couplings to Gaussian curvature not found in a rigid flat…
We consider the Klein-Gordon equation on a Riemannian surface which is globally well-posed in the energy space. This equation has an homoclinic orbit to the origin, and in this paper we study the dynamics close to it. Using a strategy from…
An integral representation for form-factors of exponential fields in the sine-Gordon model is proposed.
In this paper, using a novel approach involving the truncated Laurent expansion in the Painlev\'e analysis of the (2+1) dimensional K-dV equation, we have trilinearized the evolution equation and obtained rather general classes of solutions…
Within this article one finds the statement of the Klein-Gordon problem within the real Hilbert space formalism ($\mathbbm R$HS) in terms of complex wave functions, and in terms of quaternionic wave functions as well. The complex…
Grothendieck polynomials are important objects in the study of the $K$-theory of flag varieties. Their many remarkable properties have been studied in the context of algebraic geometry and tableaux combinatorics. We explore a new tool,…
The Adler-Kostant-Symes theorem yields isospectral hamiltonian flows on the dual $\tilde\grg^{+*}$ of a Lie subalgebra $\tilde\grg^+$ of a loop algebra $\tilde\grg$. A general approach relating the method of integration of Krichever,…
We state theoretical properties for $k$-means clustering of Symmetric Positive Definite (SPD) matrices, in a non-Euclidean space, that provides a natural and favourable representation of these data. We then provide a novel application for…
A $k$-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are…
We develop a unified approach for construction of symplectic forms for 1D integrable equations with the periodic and rapidly decaying initial data. As an example we consider the cubic nonlinear Schr\"{o}dinger equation.
In [1], the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This…
In this work we define a deformation theory for the Coupled K\"ahler-Yang-Mills equations in arXiv:1102.0991, generalizing work of Sz\'ekelyhidi on constant scalar curvature K\"ahler metrics. We use the theory to find new solutions of the…
The complex orthogonal and symplectic groups both act on the complete flag variety with finitely many orbits. We study two families of polynomials introduced by Wyser and Yong representing the $K$-theory classes of the closures of these…
K-theoretic Donaldson invariants are holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 sheaves on surfaces. We develop an algorithm which determines the generating functions of K-theoretic Donaldson…