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

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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.

Original languageEnglish (US)
Article number425101
JournalJournal of Physics A: Mathematical and Theoretical
Volume44
Issue number42
DOIs
StatePublished - Oct 21 2011

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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