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Traveling waves for nonlinear Schrödinger equations (2406.03910v1)
Published 6 Jun 2024 in math.AP
Abstract: We look for traveling wave solutions to the nonlinear Schr\"odinger equation with a subsonic speed, covering several physical models with Sobolev subcritical nonlinear effects. Our approach is based on a variant of Sobolev-type inequality involving the momentum and we show the existence of its minimizers solving the nonlinear Schr\"odinger equation.
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