skip to main content

Title: Ground states of nonlinear Schrödinger systems with saturable nonlinearity in R{sup 2} for two counterpropagating beams

Counterpropagating optical beams in nonlinear media give rise to a host of interesting nonlinear phenomena such as the formation of spatial solitons, spatiotemporal instabilities, self-focusing and self-trapping, etc. Here we study the existence of ground state (the energy minimizer under the L{sup 2}-normalization condition) in two-dimensional (2D) nonlinear Schrödinger (NLS) systems with saturable nonlinearity, which describes paraxial counterpropagating beams in isotropic local media. The nonlinear coefficient of saturable nonlinearity exhibits a threshold which is crucial in determining whether the ground state exists. The threshold can be estimated by the Gagliardo-Nirenberg inequality and the ground state existence can be proved by the energy method, but not the concentration-compactness method. Our results also show the essential difference between 2D NLS equations with cubic and saturable nonlinearities.
Authors:
 [1] ;  [2] ;  [3] ;  [2] ;  [4]
  1. Institute of Applied Mathematical Sciences and Mathematics Division, National Center for Theoretical Sciences (NCTS) at Taipei, National Taiwan University, Taipei 10617, Taiwan (China)
  2. Texas A and M University at Qatar, P.O. Box 23874, Doha (Qatar)
  3. Institute of Physics, P.O. Box 57, 11001 Belgrade (Serbia)
  4. (United States)
Publication Date:
OSTI Identifier:
22251581
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BEAMS; GROUND STATES; INSTABILITY; NONLINEAR PROBLEMS; SOLITONS; TRAPPING