ON THE CAUCHY PROBLEM FOR A NONLOCAL NONLINEAR SCHRÖDINGER EQUATION
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Date
2022-12
Authors
Wang, Hongwei
Esfahani, Amin
Journal Title
Journal ISSN
Volume Title
Publisher
Discrete and Continuous Dynamical Systems
Abstract
This paper considers the one-dimensional Schrödinger equation with nonlocal nonlinearity that describes the interactions of nonlinear dispersive waves. We obtain some the local well-posedness and ill-posedness result associated with this equation in the Sobolev spaces. Moreover, we prove the existence of standing waves of this equation. As corollary, we derive the conditions under which the solutions are uniformly bounded in the energy space.
Description
Keywords
Type of access: Open Access, Schrödinger equation, Well-posedness, Standing wave
Citation
Wang, H., & Esfahani, A. (2022). On the Cauchy problem for a nonlocal nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 27(12), 7185. https://doi.org/10.3934/dcdsb.2022039