Variational properties of space-periodic standing waves of nonlinear Schrödinger equations with general nonlinearities
Perla Kfoury,
Stefan Le Coz
Abstract:Periodic waves are standing wave solutions of nonlinear Schrödinger equations whose profile is periodic in space dimension one. We consider general nonlinearities and provide variational characterizations for the periodic wave profiles. This involves minimizing energy while keeping mass and momentum constant, as well as minimizing the action over the Nehari manifold. These variational approaches are considered both in the periodic and anti-periodic settings, and for focusing and defocusing nonlinearities. In a… Show more
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