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.

I also studied a general framework for the Poisson’s recurrence for Hamiltonian equations and their numerical time discretizations.

More recently I addressed the $p$-Schrödinger equation for the modelling of Newton’s cradle.

My PhD thesis deals with the theme, as well as part of my Habilitation thesis.

Other
Brigitte Bidegaray-Fesquet
Brigitte Bidegaray-Fesquet
Researcher

Publications

From Newton's cradle to the discrete p-Schrödinger equation
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
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On the propagation of an optical wave in a photorefractive medium
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
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A non local Schrödinger model for the propagation of waves in a photorefractive medium
We present various mathematical results (Cauchy problem, solitary waves) for the Zozulya–Anderson model which describes the …
Brigitte Bidegaray-Fesquet
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Contributions à l'électromagnétisme dans le domaine temporel. Modélisation classique et quantique en optique non linéaire
Brigitte Bidégaray
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The Cauchy Problem for Schrödinger-Debye equations
In this article we study the local-in-time Cauchy problem for the Schrödinger-Debye equations. This model occurs in nonlinear optics …
Brigitte Bidégaray
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On the Cauchy problem for some systems occurring in nonlinear optics
We study the Cauchy problem for two systems of equations (Maxwell-Debye and Maxwell-Bloch) describing laser-matter interaction …
Brigitte Bidégaray
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A perturbative analysis of the time-envelope approximation in strong Langmuir turbulence
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
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On a nonlocal Zakharov equation
Brigitte Bidégaray
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Invariant measures for some partial differential equations
We construct invariant measures for Hamiltonian systems such as the nonlinear Schrrdinger equation or the wave equation in order to …
Brigitte Bidégaray
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Etude qualitative d'équations d'ondes dispersives
Cette thèse comporte trois parties traitant différents aspects de l’étude des équations d’ondes dispersives. Les modèles …
Brigitte Bidégaray
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Etude d'équations intervenant en optique non linéaire
On étudie le problème de Cauchy associé à deux systèmes d’équations (Maxwell-Debye et Maxwell-Bloch) décrivant des phénomènes …
Brigitte Bidégaray
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On a nonlocal Zakharov equation
This article deals with the Cauchy problem for a nonlocal Zakharov equation. We will first recall the physical motivation (due to V.E. …
Brigitte Bidégaray
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