Open AccessOn the Cauchy problem for a nonlocal nonlinear Schrödinger equation
Author(s) -
Hongwei Wang,
Amin Esfahani
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022039
Subject(s) - sobolev space , bounded function , corollary , mathematics , nonlinear schrödinger equation , initial value problem , nonlinear system , mathematical analysis , cauchy problem , space (punctuation) , schrödinger equation , cauchy distribution , energy (signal processing) , physics , pure mathematics , quantum mechanics , computer science , operating system , statistics
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.