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

Journal Article · Wed Jan 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4862190· OSTI ID:22251581

Lin, Tai-Chia ^[1]; Belić, Milivoj R. ^[2]; Petrović, Milan S. ^[3]; Chen, Goong ^[2]

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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)

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.

• OSTI ID: 22251581
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEAMS
GROUND STATES
INSTABILITY
NONLINEAR PROBLEMS
SOLITONS
TRAPPING