Matrice de scattering et résonances associées à une orbite hétérocline
New polynomials for which has a solution with almost all real zeros.
Nonclassical Sturm-Liouville problems and Schrödinger operators on radial trees.
Non-self-adjoint singular Sturm-Liouville problems with boundary conditions dependent on the eigenparameter.
Numerical computation of solitons for optical systems
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large are large nonlinear exponents . In a second part, we compute...
Numerical computation of solitons for optical systems
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number k of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large k are large nonlinear exponents σ. In a second part, we compute...
On a q-deformed harmonic oscillator with variable linear momentum.
On an example of phase-space tunneling
On an inverse scattering problem for a discontinuous Sturm-Liouville equation with a spectral parameter in the boundary condition.
On Bojarski's index formula for nonsmooth interfaces.
On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem.
On the basis property of the root functions of differential operators with matrix coefficients
We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas, we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions of the operator under consideration forms a Riesz basis.
On the differential operators with periodic matrix coefficients.
On the essential spectra of matrix operators and applications.
On the essential spectrum of Dirac operators with spherically symmetric potentials.
On the genericity of nonvanishing instability intervals in periodic Dirac systems
On the -solutions to general second-order nonsymmetric differential equations.
On the Lyapunov exponent and exponential dichotomy for the quasi-periodic Schrödinger operator
In this paper we study the Lyapunov exponent for the one-dimensional Schrödinger operator with a quasi-periodic potential. Let be the set of frequency vectors whose components are rationally independent. Let , and consider the complement in of the set where exponential dichotomy holds. We show that is generic in this complement. The methods and techniques used are based on the concepts of rotation number and exponential dichotomy.
On the singular spectrum for adiabatic quasiperiodic Schrödinger operators.
On the singular spectrum of discrete Schrödinger operator