Cauchy problem for dispersive equations
Sep 1, 1991

I have been interested in the local or global in time Cauchy problem in some Sobolev spaces for various dispersive equations in the class of non-linear Schrödinger equations coupled to matter equations. Some asymptotic limit equations have been investigated.
- Debye or Bloch matter in optics.
- Zakharov model for plasmas.
- Zozulya-Anderson model for photorefractive media.
I also studied a general framework for the Poisson’s recurrence for Hamiltonian equations and their numerical time discretizations.
- Journal papers: A-Bid95b
More recently I addressed the $p$-Schrödinger equation for the modelling of Newton’s cradle.
- Journal papers: A-BDJ13
My PhD thesis deals with the theme, as well as part of my Habilitation thesis.
Publications
We investigate the dynamics of a chain of oscillators coupled by fully-nonlinear interaction potentials. This class of models includes …
Brigitte Bidegaray-Fesquet,
Eric Dumas,
Guillaume James
The aim of this paper is first to review the derivation of a model describing the propagation of an optical wave in a photorefractive …
Brigitte Bidegaray-Fesquet,
Jean-Claude Saut
We present various mathematical results (Cauchy problem, solitary waves) for the Zozulya–Anderson model which describes the …
Brigitte Bidegaray-Fesquet
Brigitte Bidégaray
In this article we study the local-in-time Cauchy problem for the Schrödinger-Debye equations. This model occurs in nonlinear optics …
Brigitte Bidégaray
We study the Cauchy problem for two systems of equations (Maxwell-Debye and Maxwell-Bloch) describing laser-matter interaction …
Brigitte Bidégaray
We investigate a nonlinear set of coupled-wave equations describing the inertial regime of the strong Langmuir turbulence, namely …
Luc Bergé,
Brigitte Bidégaray,
Thierry Colin
We construct invariant measures for Hamiltonian systems such as the nonlinear Schrrdinger equation or the wave equation in order to …
Brigitte Bidégaray
Cette thèse comporte trois parties traitant différents aspects de l’étude des équations d’ondes dispersives. Les modèles …
Brigitte Bidégaray