The solution of general KdV equation in a class of steplike functions.
The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations
The Stieltjes spectral matrix measure of the doubly infinite Jacobi matrix associated with a Toda -soliton is computed, using Sato theory. The result is used to give an explicit expansion of the fundamental solution of some discrete heat equations, in a series of Jackson’s -Bessel functions. For Askey-Wilson type solitons, this expansion reduces to a finite sum.
The Spectrum of Jacobi Matrices.
The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI
Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...
The Theory of differential invariance and infinite dimensional Hamiltonian evolutions
In this paper we describe the close relationship between invariant evolutions of projective curves and the Hamiltonian evolutions of Adler, Gel'fand and Dikii. We also show how KdV evolutions are related as well to invariant evolutions of projective surfaces.
The theory of differential invariants and KDV hamiltonian evolutions
Time-like isothermic surfaces associated to Grassmannian systems.
Trajectoires bornées d'une particule soumise à un champ magnétique symétrique linéaire
Transformation operators for the perturbed Hill difference equation and one of their applications.
Transformations between surfaces in with flat normal and/or tangent bundles.
Transformations for hypersurfaces with vanishing Gauss-Kronecker curvature.
Transparent potentials and hamiltonian systems
Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems
This text is a survey of recent results on traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity. We present the existence, nonexistence and stability results and we describe the main ideas used in proofs.
Treibich-Verdier potentials and the stationary (m)KDV hierarchy.
Two point correlation functions for a periodic box-ball system.
Two remarks about the connection of Jacobi and Neumann integrable systems.
Two-field integrable evolutionary systems of the third order and their differential substitutions.
Type des points fixes des difféomorphismes symplectiques de
Tzitzeica-Bäcklund theorems.