Gap solitons in almost periodic one-dimensional structures
Copyright policy )Gap solitons in almost periodic one-dimensional structures
We consider almost periodic stationary nonlinear Schr��dinger equations in dimension $1$. Under certain assumptions we prove the existence of nontrivial finite energy solutions in the strongly indefinite case. The proof is based on a carefull analysis of the energy functional restricted to the so-called generalized Nehari manifold, and the existence and fine properties of special Palais-Smale sequences. As an application, we show that certain one dimensional almost periodic photonic crystals possess gap solitons for all prohibited frequencies.
- Morgan State University United States
Nehari manifold, Composite media; random media in optics and electromagnetic theory, 34C37, 35Q60, 58E05, 78A48, Applications of variational problems in infinite-dimensional spaces to the sciences, FOS: Physical sciences, Mathematical Physics (math-ph), Homoclinic and heteroclinic solutions to ordinary differential equations, finite energy solutions, Mathematics - Analysis of PDEs, Soliton solutions, almost periodic stationary nonlinear Schrödinger equations in dimension 1, FOS: Mathematics, PDEs in connection with optics and electromagnetic theory, Palais-Smale sequences, Mathematical Physics, Analysis of PDEs (math.AP)
Nehari manifold, Composite media; random media in optics and electromagnetic theory, 34C37, 35Q60, 58E05, 78A48, Applications of variational problems in infinite-dimensional spaces to the sciences, FOS: Physical sciences, Mathematical Physics (math-ph), Homoclinic and heteroclinic solutions to ordinary differential equations, finite energy solutions, Mathematics - Analysis of PDEs, Soliton solutions, almost periodic stationary nonlinear Schrödinger equations in dimension 1, FOS: Mathematics, PDEs in connection with optics and electromagnetic theory, Palais-Smale sequences, Mathematical Physics, Analysis of PDEs (math.AP)
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