Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations

A. S. Desyatnikov, D. E. Pelinovsky, J. Yang

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A Hamiltonian system of incoherently coupled nonlinear Schrödinger (NLS) equations is considered in the context of physical experiments in photorefractive crystals and Bose-Einstein condensates. Due to the incoherent coupling, the Hamiltonian system has a group of various symmetries that include symmetries with respect to gauge transformations and polarization rotations. We show that the group of rotational symmetries generates a large family of vortex solutions that generalize scalar vortices, vortex pairs with either double or hidden charge, and coupled states between solitons and vortices. Novel families of vortices with different frequencies and vortices with different charges at the same component are constructed and their linearized stability problem is block-diagonalized for numerical analysis of unstable eigenvalues.

Original languageEnglish
Pages (from-to)3091-3111
Number of pages21
JournalJournal of Mathematical Sciences
Volume151
Issue number4
DOIs
Publication statusPublished - Jun 1 2008
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations'. Together they form a unique fingerprint.

  • Cite this