Vol. 8, No. 2, 2015
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Smooth parametric dependence of asymptotics of the semiclassical focusing NLS

Sergey Belov and Stephanos Venakides
Vol. 8 (2015), No. 2, 257–288
DOI: 10.2140/apde.2015.8.257
Abstract

We consider the one-dimensional focusing (cubic) nonlinear Schrödinger equation (NLS) in the semiclassical limit with exponentially decaying complex-valued initial data, whose phase is multiplied by a real parameter. We prove smooth dependence of the asymptotic solution on the parameter. Numerical results supporting our estimates of important quantities are presented.

Keywords
NLS, semiclassical limit, Riemann–Hilbert problems
Mathematical Subject Classification 2010
Primary: 37K15, 37K40
Secondary: 35P25
Milestones
Received: 29 November 2012
Revised: 13 June 2014
Accepted: 9 January 2015
Published: 10 May 2015
Authors
Sergey Belov
Department of Mathematics
University of Houston
4800 Calhoun Rd.
Houston, TX 77204-2008
United States
Stephanos Venakides
Department of Mathematics
Duke University
Box 90320
Durham, NC 27708
United States