Existence of steady-state solutions in a nonlinear photonic lattice model

Many careful experimental observations to nonlinear photonic lattice model have been constructed. In this paper, we use the principle of variational method, mountain pass lemma, fixed point method to develop an existence theorem for the steady-state solutions of a nonlinear photonic lattice model de...

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Bibliographic Details
Published in:Journal of mathematical physics 2011-06, Vol.52 (6), p.063508-063508-12
Main Authors: Chen, Shouxin, Lei, Yuqiong
Format: Article
Language:English
Subjects:
Atoms & subatomic particles
Crystals
Exact sciences and technology
Lattice theory
Mathematical methods in physics
Mathematics
Physics
Quantum physics
Sciences and techniques of general use
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Summary:Many careful experimental observations to nonlinear photonic lattice model have been constructed. In this paper, we use the principle of variational method, mountain pass lemma, fixed point method to develop an existence theorem for the steady-state solutions of a nonlinear photonic lattice model describing the propagation of a light wave in a photo-refractive crystal is established, which demonstrates that there is an amount of continuous energy that allows the existence of steady-state solutions. Our results provide a theoretical principles for a variety of experiments and research on photonic lattices and crystals. Finally, it is straightforward to see that the applicability of the present to constructing arbitrarily small energy solutions is also guaranteed.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3595692