NLS equation

Tuesday, November 1, 2016 - 9:00am - 9:50am
Eduard-Wilhelm Kirr (University of Illinois at Urbana-Champaign)
I will discuss classical and recent results regarding asymptotic stability of solitary waves i.e., localized solutions of nonlinear wave equations propagating without changing shape. Begining with the work of Soffer and Weinstein in the ’90 we know that, under certain assumptions, solutions starting close to a solitary wave shadow nearby solitary waves before collapsing on one. The mathematical analysis relies on using dispersive estimates for the linearized dynamics at a fixed (rather arbitrarily chosen) solitary wave to control the nonlinearity.
Monday, October 31, 2016 - 10:15am - 11:05am
Mark Hoefer (University of Colorado)
Quantum tunneling corresponds to the transmission of a particle with non-negligible probability through a barrier that a classical particle could not pass. This linear concept has previously been generalized to nonlinear waves and solitons incident upon an externally imposed barrier. Here, the concept of hydrodynamic tunneling is introduced whereby solitons can be transmitted through nonlinear wavetrains of hydrodynamic origin.
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