TY - JOUR
T1 - Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation
AU - Bittencourt Moraes, Gabriel E.
AU - Borluk, Handan
AU - de Loreno, Guilherme
AU - Muslu, Gulcin M.
AU - Natali, Fábio
N1 - Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/12/25
Y1 - 2022/12/25
N2 - In this paper, the existence and orbital stability of the periodic standing wave solutions for the nonlinear fractional Schrödinger (fNLS) equation with cubic nonlinearity is studied. The existence is determined by using a minimizing constrained problem in the complex setting and it is showed that the corresponding real solution is always positive. The orbital stability is proved by combining some tools regarding the oscillation theorem for fractional Hill operators and the Vakhitov-Kolokolov condition, well known for Schrödinger equations. We then perform a numerical approach to generate the periodic standing wave solutions of the fNLS equation by using the Petviashvili's iteration method. We also investigate the Vakhitov-Kolokolov condition numerically which cannot be obtained analytically for some values of the order of the fractional derivative.
AB - In this paper, the existence and orbital stability of the periodic standing wave solutions for the nonlinear fractional Schrödinger (fNLS) equation with cubic nonlinearity is studied. The existence is determined by using a minimizing constrained problem in the complex setting and it is showed that the corresponding real solution is always positive. The orbital stability is proved by combining some tools regarding the oscillation theorem for fractional Hill operators and the Vakhitov-Kolokolov condition, well known for Schrödinger equations. We then perform a numerical approach to generate the periodic standing wave solutions of the fNLS equation by using the Petviashvili's iteration method. We also investigate the Vakhitov-Kolokolov condition numerically which cannot be obtained analytically for some values of the order of the fractional derivative.
KW - Existence and uniqueness of minimizers
KW - Fractional Schrödinger equation
KW - Orbital stability
KW - Small-amplitude periodic waves
UR - http://www.scopus.com/inward/record.url?scp=85138500911&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2022.09.015
DO - 10.1016/j.jde.2022.09.015
M3 - Article
AN - SCOPUS:85138500911
SN - 0022-0396
VL - 341
SP - 263
EP - 291
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -