On the modulational instability of the nonlinear Schrödinger equation with dissipation

Z. Rapti, P. G. Kevrekidis, D. J. Frantzeskakis, B. A. Malomed

Research output: Contribution to journalConference articlepeer-review


The modulational instability (MI) of spatially uniform states in the nonlinear Schrödinger (NLS) equation is examined in the presence of higher-order dissipation. The study is motivated by results on the effects of three-body recombination in Bose-Einstein condensates (BECs), as well as by the important recent work of Segur et al. on the effects of linear damping in NLS settings. We show how the presence of even the weakest possible dissipation suppresses the instability on a longer time scale. However, on a shorter scale, the instability growth may take place, and a corresponding generalization of the MI criterion is developed. The analytical results are corroborated by numerical simulations. The method is valid for any power-law dissipation form, including the constant dissipation as a special case.

Original languageEnglish (US)
Pages (from-to)74-77
Number of pages4
JournalPhysica Scripta T
StatePublished - 2004
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics

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