Hamiltonian Hopf bifurcations and dynamics of NLS/GP standing-wave modes

Document Type

Article

Publication Date

10-21-2011

Abstract

We examine the dynamics of solutions to nonlinear Schrödinger/ GrossPitaevskii equations that arise due to semisimple indefinite Hamiltonian Hopf bifurcations-the collision of pairs of eigenvalues on the imaginary axis. We construct localized potentials for this model which lead to such bifurcations in a predictable manner. We perform a formal reduction from the partial differential equations to a small system of ordinary differential equations. We analyze the equations to derive conditions for this bifurcation and use averaging to explain certain features of the dynamics that we observe numerically. A series of careful numerical experiments are used to demonstrate the phenomenon and the relations between the full system and the derived approximations. © 2011 IOP Publishing Ltd.

Identifier

80053608139 (Scopus)

Publication Title

Journal of Physics A Mathematical and Theoretical

External Full Text Location

https://doi.org/10.1088/1751-8113/44/42/425101

e-ISSN

17518121

ISSN

17518113

Issue

42

Volume

44

Grant

0807284

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS