Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap

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Abstract

We consider the long-term weakly nonlinear evolution governed by the two-dimensional nonlinear Schr\"{o}dinger (NLS) equation with an isotropic harmonic oscillator potential. The dynamics in this regime is dominated by resonant interactions between quartets of linear normal modes, accurately captured by the corresponding resonant Hamiltonian system. In the framework of this system, we identify Fermi-Pasta-Ulam-like recurrence phenomena, whereby the normal-mode spectrum passes in close proximity of the initial configuration, and two-mode states with time-independent mode amplitude spectra that translate into long-lived breathers of the original NLS equation. We comment on possible implications of these findings for nonlinear optics and matter-wave dynamics in Bose-Einstein condensates.
Original languageEnglish
Article number034210
Number of pages16
JournalPhys. Rev. E
Volume104
Issue number3
DOIs
Publication statusPublished - 13 Sep 2021

Bibliographical note

v2: cosmetic improvements, published version

Keywords

  • nlin.PS
  • cond-mat.quant-gas
  • math-ph
  • math.MP

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