Breaking In The Semiclassical Solution Of The Focusing Nonlinear Schrodinger Equation
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Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154)
Author: Spyridon Kamvissis
language: en
Publisher: Princeton University Press
Release Date: 2003-09-07
Providing an asymptotic analysis via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime, this text exploits complete integrability to establish pointwise asymptotics for this problem's solution.
Breaking in the Semiclassical Solution of the Focusing Nonlinear Schrodinger Equation
We study the one dimensional semiclassical focusing cubic nonlinear Schrodinger equation with a one parameter family of decaying initial conditions using the Lax pair and the Riemann-Hilbert approach to inverse scattering. In previous studies the solution was found to develop fast oscillations in modulus passed some curves in the space-time plane (breaking curves or nonlinear caustics). We carried out a detailed asymptotic analysis of the solution as we approach a catastrophic break of the our analytic procedure. We developed numerical integration on a Riemann surface to compute the relevant quantities numerically near the catastrophic break and providing new insights to the first break.
Nonlinear Wave Equations
Author: Christopher W. Curtis
language: en
Publisher: American Mathematical Soc.
Release Date: 2015-03-26
This volume contains the proceedings of the AMS Special Session on Nonlinear Waves and Integrable Systems, held on April 13-14, 2013, at the University of Colorado, Boulder, Colorado. The field of nonlinear waves is an exciting area of modern mathematical research that also plays a major role in many application areas from physics and fluids. The articles in this volume present a diverse cross section of topics from this field including work on the Inverse Scattering Transform, scattering theory, inverse problems, numerical methods for dispersive wave equations, and analytic and computational methods for free boundary problems. Significant attention to applications is also given throughout the articles with an extensive presentation on new results in the free surface problem in fluids. This volume will be useful to students and researchers interested in learning current techniques in studying nonlinear dispersive systems from both the integrable systems and computational points of view.