36 citations · 140 across the 12 of their papers we have counts for
16 papers
Variational properties of space-periodic standing waves of nonlinear Schr{ö}dinger equations with general nonlinearities
Perla Kfoury, Stefan Le Coz
Periodic waves are standing wave solutions of nonlinear Schr\''odinger equations whose profile is periodic in space dimension one. We consider general nonlinearities and provide va…
Computation of excited states for the nonlinear Schr{ö}dinger equation: numerical and theoretical analysis
Christophe Besse, Romain Duboscq, Stefan Le Coz
Our goal is to compute excited states for the nonlinear Schr{ö}dinger equation in the radial setting. We introduce a new technique based on the Nehari manifold approach and give a…
A minimal mass blow-up solution on a nonlinear quantum star graph
François Genoud, Stefan Le Coz, Julien Royer
We construct a finite-time blow-up solution to the mass-critical focusing nonlinear Schrödinger equation on a metric star graph with an arbitrary number of edges. We show that all…
Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schr{ö}dinger equation
Perla Kfoury, Stefan Le Coz, Tai-Peng Tsai
For the double power one dimensional nonlinear Schr{ö}dinger equation, we establish a complete classification of the stability or instability of standing waves with positive freque…
Gradient Flow Approach to the Calculation of Stationary States on Nonlinear Quantum Graphs
Christophe Besse, Romain Duboscq, Stefan Le Coz
We introduce and implement a method to compute stationary states of nonlinear Schr\''odinger equations on metric graphs. Stationary states are obtained as local minimizers of the n…
On the Cauchy problem and the black solitons of a singularly perturbed Gross-Pitaevskii equation
Isabella Ianni, Stefan Le Coz, Julien Royer
We consider the one-dimensional Gross-Pitaevskii equation perturbed by a Dirac potential. Using a fine analysis of the properties of the linear propagator, we study the well-posedn…
Finite and infinite soliton and kink-soliton trains of nonlinear Schrödinger equations
Stefan Le Coz, Tai-Peng Tsai
We will first review known results on multi-solitons of dispersive partial differential equations, which are special solutions behaving like the sum of many weakly-interacting soli…
Minimal mass blow up solutions for a double power nonlinear Schrödinger equation
Stefan Le Coz, Yvan Martel, Pierre Raphael
We consider a nonlinear Schrödinger equation with double power nonlinearity, where one power is focusing and mass critical and the other mass sub-critical. Classical variational ar…
Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations
Stefan Le Coz, Tai-Peng Tsai
We look for solutions to generic nonlinear Schrödinger equations build upon solitons and kinks. Solitons are localized solitary waves and kinks are their non localized counter-part…
Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations
Stefan Le Coz, Dong Li, Tai-Peng Tsai
We study *infinite soliton trains* solutions of nonlinear Schrödinger equations (NLS), i.e. solutions behaving at large time as the sum of infinitely many solitary waves. Assuming…
Multi-solitary waves for the nonlinear Klein-Gordon equation
Jacopo Bellazzini, Marco Ghimenti, Stefan Le Coz
We consider the nonlinear Klein-Gordon equation in . We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the…
Multi-Speeds solitary waves solutions for nonlinear Schrödinger systems
Isabella Ianni, Stefan Le Coz
We prove the existence of a new type of solutions to a nonlinear Schrödinger system. These solutions, which we call "multi-speeds solitary waves", are behaving at large time as a c…
On the stability of standing waves of Klein-Gordon equations in a semiclassical regime
Marco Ghimenti, Stefan Le Coz, Marco Squassina
We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.
High speed excited multi-solitons in nonlinear Schrödinger equations
Raphaël Cote, Stefan Le Coz
We consider the nonlinear Schrödinger equation with a general nonlinearity. In dimension higher than 2, this equation admits travelling wave solutions with a fixed profile which is…
Instability for standing waves of nonlinear Klein-Gordon equations via mountain-pass arguments
Louis Jeanjean, Stefan Le Coz
We introduce mountain-pass type arguments in the context of orbital instability for Klein-Gordon equations. Our aim is to illustrate on two examples how these arguments can be usef…
A note on Berestycki-Cazenave's classical instability result for nonlinear Schrödinger equations
Stefan Le Coz
In this note we give an alternative, shorter proof of the classical result of Berestycki and Cazenave on the instability by blow-up for the standing waves of some nonlinear Schrödi…