Vol. 1, No. 3, 2008

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Dynamics of nonlinear Schrödinger/Gross–Pitaevskii equations: mass transfer in systems with solitons and degenerate neutral modes

Zhou Gang and Michael I. Weinstein

Vol. 1 (2008), No. 3, 267–322
Abstract

Nonlinear Schrödinger/Gross–Pitaevskii equations play a central role in the understanding of nonlinear optical and macroscopic quantum systems. The large time dynamics of such systems is governed by interactions of the nonlinear ground state manifold, discrete neutral modes (“excited states”) and dispersive radiation. Systems with symmetry, in spatial dimensions larger than one, typically have degenerate neutral modes. Thus, we study the large time dynamics of systems with degenerate neutral modes. This requires a new normal form (nonlinear matrix Fermi Golden Rule) governing the system’s large time asymptotic relaxation to the ground state (soliton) manifold.

Keywords
soliton, nonlinear bound state, nonlinear scattering, asymptotic stability, dispersive partial differential equation
Mathematical Subject Classification 2000
Primary: 35Q51, 37K40, 37K45
Milestones
Received: 9 January 2008
Revised: 14 July 2008
Accepted: 22 October 2008
Published: 18 December 2008
Authors
Zhou Gang
Department of Mathematics
Princeton University
Princeton, NJ
United States
Michael I. Weinstein
Department of Applied Physics and Applied Mathematics
Columbia University
New York, NY 10027
United States
http://www.columbia.edu/~miw2103/