Emerging Applications of the Nonlinear Schrödinger Equations - IPAM

Emerging Applications of the Nonlinear Schrödinger Equations

February 3 - 7, 2003

Schedule

All times in this Schedule are Pacific Time (PT)

Monday, February 3, 2003

Morning Session

00:00-00:00
Day 1: Laser propagation in bulk medium
Session Chair: Shi Jin
08:30-09:00
Check-In/Light Breakfast (Hosted by IPAM)
09:00-10:00
Alexander Gaeta (Cornell University)
Spatial and Temporal Dynamics of Nonlinear Wave Collapse
10:00-11:00
Alfred Vogel (Medizinisches Laserzentrum Lübeck, Germany)
Numerical simulations of optical breakdown for cellular laser surgery at nanosecond to femtosecond time scales
11:00-11:30
Break
11:30-12:30
Pierre-Louis Sulem (Obervatoire de la Cote d'Azur)
Wave collapse in dispersive magnetohydrodynamics: direct simulations and asymptotic modeling

Afternoon Session

12:30-14:00
Lunch (on your own)
Session Chair: Pierre-Louis Sulem
14:00-15:00
Xiao-Ping Wang (Hong Kong University of Science and Technology)
An adaptive grid method for singular problems and applications
15:00-15:30
Break
15:30-16:30
Boaz Ilan (University of Colorado)
Self-focusing and multiple filamentation of circularly polarized beams
16:30-17:30
Miroslav Kolesik (University of Arizona)
Unidirectional optical pulse propagation equations - from Maxwell to Nonlinear Schrödinger equation
17:30-19:00
Wine/Cheese Reception (Hosted by IPAM)

Tuesday, February 4, 2003

Morning Session

00:00-00:00
Day 2: 2D NLS theory
Session Chair: Catheleen Sulem
09:00-10:00
Frank Merle (Universite de Cergy, France)
qualitative description of blow-up for critical NLS
10:00-11:00
Gadi Fibich (Tel-Aviv University, Israel)
Nonlinear Schrödinger equations with fourth-order dispersion
11:00-11:30
Break
11:30-12:30
Hayato Nawa (Nagoya University)
Title not available

Afternoon Session

12:30-14:00
Lunch (on your own)
Session Chair: Gadi Fibich
14:00-15:00
Semyon Tsynkov (North Carolina State University)
Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves
15:00-15:30
Break
15:30-16:30
Yvan Martel (Ecole Polytechnique, France)
Blow up phenomenon in the energy space for the critical generalized KdV equation
16:30-17:30
Jared Bronski (University of Illinois at Urbana-Champaign)
Instability and Pattern formation in a nonlocal NLS

Wednesday, February 5, 2003

Morning Session

00:00-00:00
Day 3: Solitons+communications
Session Chair: Michael Weinstein
09:00-10:00
Ziad Musslimani (University of Colorado)
The vector nonlinear Schrödinger equations
10:00-11:00
George Stegeman (University of Central Florida)
Optical Experiments with the Discrete Nonlinear Schrödinger Equation
11:00-11:30
Break
11:30-12:30
Rick Trebino (Georgia Institute of Technology)
Measurements of Ultrafast Continuum Generation in Microstructure Fiber

Afternoon Session

12:30-14:00
Lunch (on your own)
Session Chair: George Papanicolaou
14:00-15:00
Michael Weinstein (Bell Laboratories)
Selection of the ground state for nonlinear Schrödinger Equations
15:00-15:30
Break
15:30-16:30
Mark Ablowitz (University of Colorado)
Discrete and continuous nonlinear Schrödinger systems
16:30-17:30
Peter Markowich (Universität Wien)
PDE Models for Bose-Einstein Condensation

Thursday, February 6, 2003

Morning Session

00:00-00:00
Day 4: Solitons+communications (continued)
Session Chair: Mark Ablowitz
09:00-10:00
William Kath (Northwestern University)
Simulating rare events in optical transmission systems
10:00-11:00
Alejandro Aceves (University of New Mexico)
Pulse dynamics in nonlinear photonic crystal fibers and periodic structures
11:00-11:30
Break
11:30-12:30
Ildar Gabitov (University of Arizona)
Intra-Channel Four Wave Mixing in High Speed Optical Fiber Communications

Afternoon Session

12:30-14:00
Lunch (on your own)
Session Chair: Irene Gamba
14:00-15:00
Jean-Claude Diels (University of New Mexico)
Spatial-temporal solitons in air --- experimental puzzles, and (too) simple models
15:00-15:30
Break
15:30-16:30
Christopher Jones (University of North Carolina)
Perturbations of solitary waves in dispersion-managed systems
16:30-17:30
Li-Tien Cheng (University of California, San Diego (UCSD))
The Level Set Method Applied to the Schrödinger Equation
17:30-19:00
Dinner (Hosted by IPAM)

Friday, February 7, 2003

Morning Session

00:00-00:00
Day 5: BEC
Session Chair: Peter Markowich
09:00-10:00
Amandine Aftalion (École Polytechnique)
Mathematical model for Bose Einstein condensates
10:00-11:00
Qiang Du (Columbia University)
Quantized vortices in Bose-Einstein condensate
11:00-11:30
Break
11:30-12:30
Alexander Fetter (Stanford University)
Stability and Dynamics of Vortices in a Trapped Bose-Einstein Condensate

Afternoon Session

12:30-14:00
Lunch (on your own)
Session Chair: Alexander Fetter
14:00-15:00
Irene Gamba (University of Texas at Austin)
Quantum Trajectories and the Wigner equation
15:00-15:30
Break
15:30-16:30
Catherine Sulem (University of Toronto)
On asymptotic stability of solitary waves for nonlinear Schrödinger equations
16:30-17:30
Alex Gottlieb (Universität Wien)
Self-consistent Schroedinger and Liouville-von Neumann equations for material particles
17:30
Conclusion
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