We present some results around three directions: 1- Focusing at one point in nonlinear geometrical optics. The equations considered are essentially wave and Schrödinger equations. 2- Role of quadratic oscillations in nonlinear Schrödinger equations. 3- Linear vs. nonlinear effects for nonlinear Schrödinger equations with a potentiel.Nous présentons des travaux autour de trois axes : 1- Phénomène de focalisation en un point en optique géométrique non linéaire. Les équations considérées sont principalement des équations d'ondes et de Schrödinger non linéaires. 2- Rôle des oscillations quadratiques dans les équations de Schrödinger non linéaires. 3- Equations de Schrödinger non linéaire en présence d'un potentiel extérieur
Explores Schrödinger equations with power-type nonlinearity, with scattering results for mass- and e...
This thesis consists into three parts addressing various aspects of the study of dispersive wave equ...
We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. ...
Nous présentons des travaux autour de trois axes : 1- Phénomène de focalisation en un point en optiq...
AbstractWe consider a nonlinear semi-classical Schrödinger equation for which it is known that quadr...
J. Funct. Anal. 203 (2003), no. 2, 453-493We consider a nonlinear semi-classical Schrödinger equatio...
We consider a nonlinear semi-classical Schrödinger equation for which quadratic oscillations lead to...
Abstract. Oscillating approximate solutions to nonlinear hyperbolic dispersive systems are studied. ...
We survey some results on (N LSε), discussing also new perspectives and open problems
The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, in pa...
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled...
The nonlinear coupling of two scalar nonlinear Schrödinger (NLS) fields results in nonfocusing insta...
Abstract. The formation of singularities of self-focusing solutions of the nonlinear Schrödinger equ...
IntroductionThe phenomena of nonlinear optics are widely varied, both as to the nature of the nonlin...
Reported in this paper are results concerning the Cauchy problem and the dynamics for a cubic nonlin...
Explores Schrödinger equations with power-type nonlinearity, with scattering results for mass- and e...
This thesis consists into three parts addressing various aspects of the study of dispersive wave equ...
We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. ...
Nous présentons des travaux autour de trois axes : 1- Phénomène de focalisation en un point en optiq...
AbstractWe consider a nonlinear semi-classical Schrödinger equation for which it is known that quadr...
J. Funct. Anal. 203 (2003), no. 2, 453-493We consider a nonlinear semi-classical Schrödinger equatio...
We consider a nonlinear semi-classical Schrödinger equation for which quadratic oscillations lead to...
Abstract. Oscillating approximate solutions to nonlinear hyperbolic dispersive systems are studied. ...
We survey some results on (N LSε), discussing also new perspectives and open problems
The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, in pa...
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled...
The nonlinear coupling of two scalar nonlinear Schrödinger (NLS) fields results in nonfocusing insta...
Abstract. The formation of singularities of self-focusing solutions of the nonlinear Schrödinger equ...
IntroductionThe phenomena of nonlinear optics are widely varied, both as to the nature of the nonlin...
Reported in this paper are results concerning the Cauchy problem and the dynamics for a cubic nonlin...
Explores Schrödinger equations with power-type nonlinearity, with scattering results for mass- and e...
This thesis consists into three parts addressing various aspects of the study of dispersive wave equ...
We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. ...