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On a variational problem with lack of compactness related to the Strichartz inequality. (English) Zbl 1352.49002

Summary: We study a variational problem from nonlinear fiber optics which strongly lacks compactness, due to the absence of a priori bounds in spaces different from \(L^2(\mathbb R)\). A method is established how to restore this missing compactness by means of the dispersive properties inherent in the problem.

MSC:

49J10 Existence theories for free problems in two or more independent variables
49J20 Existence theories for optimal control problems involving partial differential equations
35A15 Variational methods applied to PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
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