Ground states of nonlinear Schrödinger systems with saturable nonlinearity in R2 for two counterpropagating beams
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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 twodimensional (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. © 2014 AIP Publishing LLC.
author list (cited authors)
Lin, T., Belić, M. R., Petrović, M. S., & Chen, G.