Breaking in the semiclassical solution of the focusing nonlinear Schrodinger equation
Posted on:2009-09-29
Degree:Ph.D
Type:Dissertation
University:Duke University
Candidate:Belov, Sergey M
Full Text:PDF
GTID:1440390005458555
Subject:Mathematics
Abstract/Summary:
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.