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Emerging Applications of the Nonlinear Schrödinger EquationsFebruary 3 - 7, 2003Organizing Committee:
Gadi Fibich
(Tel-Aviv University, Israel)
Scientific IntroductionThe nonlinear Schrödinger (NLS) equation provides a canonical description for the envelope dynamics of a quasi-monochromatic plane wave propagating in a weakly nonlinear dispersive medium when dissipative processes are negligible. It arises in various physical contexts in the description of nonlinear waves such as propagation of a laser beam in a medium whose index of reflection is sensitive to the wave amplitude, water waves at the free surface of an ideal and plasma waves. NLS also appears in the description of the Bose-Einstein Condensate (BEC), a context where it is often called the Gross-Pitaevskii equation. It admits solutions in the form of coherent structures like vortices that define states that can be excited in super helium. The last few years have witnessed a rapid development in research of NLS-related applications such as optical communications, laser surgeries, remote sensing and the BEC. This has created an enormous amount of new mathematical problems for mathematicians. Workshop ObjectivesThe last two decades have seen enormous amount of research activities in both mathematical analysis and applications of the NLS equations. We can foresee even more activities in this area given the potential industrial applications of NLS to optical communications, remote sensing, laser surgery, and the BEC. It is now the right time to bring together mathematicians, physicists, and people from industry to report their current research results in order to foster future collaborations and strengthen existing ones between mathematicians and non-mathematicians. This is especially important in the case of the 2D NLS, where for many years there has been little contact between mathematicians and non-mathematicians. This week-long workshop will consist of expository lectures by leaders in different disciplines, regular research presentations and panel discussions on future directions. Interactions between people from different communities will be an important component of the workshop. Topics For Discussion
SpeakersMark Ablowitz (University of Colorado)Alejandro Aceves (University of New Mexico) Amandine Aftalion (Universite Pierre et Marie Curie, Paris) Jared Bronski (University of Illinois at Urbana-Champaign) Li-Tien Cheng (University of California at San Diego) Qiang Du (Pennsylvania State University) Alexander Fetter (Stanford University) Gadi Fibich (Tel-Aviv University, Israel) Ildar Gabitov (University of Arizona) Alexander Gaeta (Cornell University) Irene Gamba (University of Texas, Austin) Alex Gottlieb (Wolfgang Pauli Institute) Boaz Ilan (University of Colorado) Christopher Jones (Brown University) William Kath (Northwestern University) Miroslav Kolesik (University of Arizona) Hailiang Liu (Iowa State University) Peter Markowich (University of Vienna and Radon Institute, Austrian Academy of Science, Linz) Yvan Martel (Ecole Polytechnique, France) Frank Merle (Universite de Cergy, France) Hayato Nawa (Nagoya University) George Stegeman (University of Central Florida) Catherine Sulem (University of Toronto) Pierre-Louis Sulem (Obervatoire de la Cote d'Azur) Rick Trebino (Georgia Institute of Technology) Semyon Tsynkov (North Carolina State University) Alfred Vogel (Medizinisches Laserzentrum Lübeck, Germany) Xiao-Ping Wang (Hong Kong University of Science and Technology) Contact Us:Institute for Pure and Applied Mathematics (IPAM) |
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