Ground states of nonlinear Schrodinger systems with saturable nonlinearity in R2 for two counterpropagating beams Academic Article uri icon


  • 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 L2-normalization condition) in two-dimensional (2D) nonlinear Schrdinger (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.

published proceedings


author list (cited authors)

  • Lin, T., Belic, M. R., Petrovic, M. S., & Chen, G.

citation count

  • 10

complete list of authors

  • Lin, Tai-Chia||Belic, Milivoj R||Petrovic, Milan S||Chen, Goong

publication date

  • January 2014