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Colin, Mathieu (Univ. de Bordeaux)  WPI, Seminar Room 08.135  Mon, 28. Sep 15, 14:30 
Solitons in quadratic media  
In this talk, we investigate the properties of solitonic structures arising in quadratic media. More precisely, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or nonelliptic systems and we address the problem of orbital stability. Finally, we present some numerical experiments in order to compute localized states for several regimes.  

Saut, JeanClaude (Univ. Paris d'Orsay)  WPI, Seminar Room 08.135  Mon, 28. Sep 15, 15:30 
Full dispersion water waves models  
We will survey recent results and open problems on various nonlocal "full dispersion" models of surface water waves.  

Dumas, Eric (Univ. de Grenoble)  WPI, Seminar Room 08.135  Tue, 29. Sep 15, 9:15 
Some variants of the focusing NLS equations Derivation, justification and open problems  
The usual model of nonlinear optics given by the cubic NLS equation is too crude to describe large intensity phenomenas such as filamentation, which modifies the focusing of laser beams. I shall explain how to derive some more appropriate variants of the NLS model from Maxwell's equations, using improved approximations of the original dispersion relation or taking ionization effects into account. I shall provide rigorous error estimates for the models considered, and also discuss some open problems related to these modified NLS equations. This is joint work with David Lannes and Jeremie Szeftel.  

González de Alaiza Martínez, Pedro (CEA)  WPI, Seminar Room 08.135  Tue, 29. Sep 15, 10:30 
Mathematical models for terahertz emissions by lasergas interaction  
Terahertz (THz) emissions have nowadays important applications such as security screening and imaging. Lasergas interaction reveals itself to be a promising technique to generate broadband and intense THz sources suitable for these applications. In this talk, I will explain recent mathematical models and their underlying physics explaining the THz radiation generated when ultrafast laser pulses ionize a gas at high intensities. Solutions to the model equations will be compared with direct numerical simulations.  

Hayashi, Nakao (Osaka Univ.)  WPI, Seminar Room 08.135  Tue, 29. Sep 15, 11:15 
Asymptotics of solutions to fourthorder nonlinear Schrödinger equations  
We consider the Cauchy problem for the fourthorder nonlinear Schrödinger equation with a critical nonlinearity and prove the asymptotic stability of solutions in the neighborhood of the self similar solutions under the non zero mass condition and the smallness on the data.  

Hirayama; Hiroyuki (Nagoya Univ.)  WPI, Seminar Room 08.135  Tue, 29. Sep 15, 14:15 
Wellposedness for a system of quadratic derivative nonlinear Schrödinger equations with periodic initial data.  
We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin as a model of laserplasma interaction. In this talk, we prove the wellposedness of this system for the periodic initial data. In particular, if the coefficients of Laplacian satisfy some conditions, then the wellposedness is proved at the scaling critical regularity by using U^2 and V^2 spaces.  

Klein, Christian (Univ. de Bourgogne)  WPI, Seminar Room 08.135  Wed, 30. Sep 15, 9:15 
Numerical study of fractional nonlinear Schrödinger equations  
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödingertype equations involving a fractional Laplacian in an onedimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub and supercritical regimes can be identified. This allows us to study the possibility of finite time blowup versus global existence, the nature of the blowup, the stability and instability of nonlinear ground states and the longtime dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.  

Le Coz, Stefan (Univ. De Toulouse)  WPI, Seminar Room 08.135  Wed, 30. Sep 15, 10:30 
On a singularly perturbed GrossPitaevskii equation  
We consider the 1D GrossPitaevskii equation perturbed by a Dirac potential. Using a fine analysis of the properties of the linear propagator, we study the wellposedness of the Cauchy Problem in the energy space of functions with modulus 1 at infinity. Then we study existence and stability of the black solitons with a combination of variational and perturbation arguments. This is a joint work with Isabella Ianni and Julien Royer.  

Melinand, Benjamin (Univ. de Bordeaux)  WPI, Seminar Room 08.135  Wed, 30. Sep 15, 11:15 
The Proudman resonance  
In this talk, I will explain the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. In order to explain this phenomenon, I will prove a local wellposedness of the water waves equations with a non constant pressure at the surface, taking into account the dependence of small physical parameters. Then, I will justify mathematically the historical work of Proudman. Finally, I will study the linear water waves equations and I will give dispersion estimates in order to extend The Proudman resonance to deeper waters. To complete these asymptotic models, I will show some numerical simulations.  

Ohta, Masahito (Science University of Tokyo)  WPI, Seminar Room 08.135  Thu, 1. Oct 15, 9:15 
Stability of standing waves for a system of nonlinear Schrodinger equations with cubic nonlinearity  
We consider a system of nonlinear Schrodinger equations with cubic nonlinearity, called a coherently coupled NLS system (CCNLS) in nonlinear optics, in one space dimension. We study orbital stability and instability of standing wave solutions of (CCNLS), and prove similar results to Colin and Ohta (2012) which studies a system of NLS equations with quadratic nonlinearity. This is a joint work with Shotaro Kawahara (Tokyo University of Science).  

Pomponio, Alessio (Politecnico di Bari)  WPI, Seminar Room 08.135  Thu, 1. Oct 15, 10:30 
BornInfeld equations in the electrostatic case  
The equation in (BI) appears for instance in the BornInfeld nonlinear electromagnetic theory: in the electrostatic case it corresponds to the Gauss law in the classical Maxwell theory and so is the electric potential and is an assigned extended charge density. We discuss existence, uniqueness and regularity of the solution of (BI). The results have been obtained in a joint work with Denis Bonheure and Pietro d’Avenia.  

Stimming, HansPeter (Univ. Wien)  WPI, Seminar Room 08.135  Thu, 1. Oct 15, 11:15 
Nonlocal NLS of derivative type for modeling highly nonlocal optical nonlinearities  
A new NLS type equation is employed for modeling longrange interactions in nonlinear optics, in a collaboration with experimental physicists. It is of quasilinear type and models fluctuations around a 'continuouswave polariton' which are chosen according to Bogoliubov theory. We present a numerical discretization method and simulation results. Mathematical theory for this equation is work in progress.  

Watanabe, Tatsuya (Kyoto Sangyo University)  WPI, Seminar Room 08.135  Fri, 2. Oct 15, 9:15 
Uniqueness and asymptotic behavior of ground states for quasilinear Schrodinger equations arising in plasma physics  
In this talk, we consider a quasiinear Schrodinger equation which appears in the study of plasma physics. We are interested in the uniqueness of ground states without assuming any restriction on a physical parameter. We also study asymptotic behavior of ground states as the parameter goes to zero.  

Texier, Benjamin (Univ. de Paris VII)  WPI, Seminar Room 08.135  Fri, 2. Oct 15, 10:30 
Spacetime resonances and highfrequency instabilities in twofluid EulerMaxwell systems  
We show that spacetime resonances induce highfrequency instabilities in the twofluid EulerMaxwell system. This implies in particular that the Zakharov approximation to EulerMaxwell is stable if and only if the group velocity vanishes. The instability proof relies on a shorttime representation formula for the flows of pseudodifferential operators of order zero. This is joint work with Eric Dumas (Grenoble) and Lu Yong (Prague).  

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