Wang, HongweiEsfahani, Amin2022-11-142022-11-142022-12Wang, 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.2022039http://nur.nu.edu.kz/handle/123456789/6765This 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.enAttribution-NonCommercial-ShareAlike 3.0 United StatesType of access: Open AccessSchrödinger equationWell-posednessStanding waveArticle