SCIENTIFIC PROGRAMS AND ACTIVITIES

November 29, 2014

May 2-5, 2011
Workshop on Wave Breaking and Global Solutions in the Short-Pulse Dispersive Equations
at the Fields Institute , 222 College Street, Toronto

Organizer: Dmitry Pelinovsky, McMaster University (Canada)

Overview

The scientific importance of very short pulses originates from applications for high power lasers and MHD/fusion devices such as Tokamaks. The classical envelope equations (such as the nonlinear Schrodinger equation) are no longer valid as the pulse width is only few carrier wavelengths, instead of thousands of these. The short-pulse equation was derived in this context as the alternative of the nonlinear Schrodinger equation to describe ultra-short pulses with fewer cycles. This equation represents the class of nonlinear dispersive wave equations with low-frequency dispersion, which reduce in the dispersionless limit to the invisid Burgers equation. Another famous member of this class is the reduced Ostrovsky equation derived in the context of surface water waves in a rotating fluid.

The five-day workshop will focus on the open problems in the wave breaking and the existence of global solutions for the short-pulse and other nonlinear dispersive wave equations. This workshop will also initiate collaborations between applied mathematicians, who are involved with the actual modeling of dispersive wave equations, and more pure analysts, who are interested in the analytic solutions of these equations.

Schedule:

Monday, May 2
9:30-10:00 On-site Registration and Morning Coffee
10:00-11:00 Alex Himonas (University of Notre Dame)
The Cauchy problem of weakly dispersive equations
11:00-12:00 Atanas Stefanov (University of Kansas)
Well-posedness and small data scattering for the generalized Ostrovsky equation
12:00-1:30 Lunch Break
1:30-2:30 John Hunter (University of California)
Waves with constant frequency
2:30-3:30 Didier Pilod (Federal University of Rio de Janeiro)
On Hirota-Satsuma's equation
3:30-4:30 Eugene Wayne (Boston University)
Asymptotic Stability of the Toda m-solitons
4:30-5:30 Zhijun Qiao (University of Texas - Pan American)
Negative order KdV equation and its soliton and kink solutions
5:30-6:30 Reception (Fields Atrium)
Tuesday, May 3
9:30-10:00 Morning Coffee
10:00-11:00 Guido Schneider (University of Stuttgart)
Why makes the NLS equation correct predictions beyond its range of validity?
11:00-12:00 Alessandro Selvitella (McMaster University)
Some problems concerning a Quasilinear Schroedinger Equation
12:00-1:30 Lunch Break
1:30-2:30 Tobias Schafer (City University of New York)
The NLSE and SPE as approximations of a nonlinear wave equation
2:30-3:30 Nathan Kutz (University of Washington)
Modeling Mode-Locked Lasers in the Few Femtosecond Regime
3:30-4:30 Yeo-Jin Chung (Southern Methodist University)
Strong Collapse Turbulence in Quintic Nonlinear Schroedinger Equation
4:30-5:30 Slim Ibrahim (University of Victoria)
On sharp scattering threshold for the focusing critical NLS & NLKG equations
6:00-8:00 Workshop Dinner
Wednesday, May 4
9:30-10:00 Morning Coffee
10:00-11:00 Mathieu Colin (University of Bordeaux)
Laser Plasma interactions: Zakharov's System and solitary waves
11:00-12:00 Walter Craig (McMaster University)
Birkhoff normal forms for the problem of water waves
12:00-2:00 Lunch Break
2:00-2:30 Seungly Oh (University of Kansas)
On quadratic Schroedinger equations in 1D: a normal form approach
2:30-3:00 Anton Sakovich (McMaster University)
Wave breaking in the Ostrovsky-Hunter equation
3:00-3:30 Coffee Break
3:30-4:30 Feride Tiglay (Fields Institute)
Integrable evolution equations on spaces of tensor densities and their peakon solutions
4:30-5:00 Edwin Ding (University of Washington)
High-Energy Passive Mode-Locking with the Sinusoidal Ginzburg-Landau Model
5:00-5:30 Matt Williams (University of Washington)
A Reduced Order Model for the Multi-Pulse Transition in Mode-Locked Lasers
Thursday, May 5
9:30-10:00 Morning Coffee
10:00-11:00 Nick Constanzino (Pennsylvania State University)
Analysis of solitary waves of the regularized short pulse equation
11:00-11:30 Levent Kurt (City University of New York)
Randomness and Stochastic Short Pulse Equation
End of Workshop

 

Final List of Participants:

Full Name University Name
Andrews, Rob (no affiliation)
Ayala, Diego McMaster University
Betti, Matthew McMaster University
Chung, Yeojin Southern Methodist University
Colin, Mathieu University of Bordeaux 1
Craig, Walter McMaster University
Ding, Edwin University of Washington
Himonas, Alex University of Notre Dame
Hunter, John K. University of California
Ibrahim, Slim University of Victoria
Kurt, Levent Baruch College, The City University of New York
Kutz, J. Nathan University of Washington
Lyaghfouri, Abdeslem University of Toronto at Mississauga
Oh, Seungly University of Kansas
Pelinovsky, Dmitry McMaster University
Pilod, Didier Universidade Federal do Rio de Janeiro - Ilha do Fundão
Ponomarev, Dmitry McMaster University
Qiao, Zhijun University of Texas-Pan American
Rogers, Nick McMaster University
Sakovich, Anton McMaster University
Schäfer, Tobias City University of New York
Schneider, Guido University of Stuttgart
Selvitella, Alessandro McMaster University
Stefanov, Atanas University of Kansas
Tiglay, Feride The Fields Institute
Wayne, C. Eugene Boston University
Williams, Matthew University of Washington



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