Author
Bittencourt Moraes, G. E., Borluk, Handan, de Loreno, G., Muslu, G. M., Natali, F.
Publication Date
2022-12-25
Publication Place
-
Elsevier
Subject
Existence and uniqueness of minimizers, Fractional Schrödinger equation, Orbital stability, Small-amplitude periodic waves
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0022-0396
Record ID
442df295-dd58-46e5-a0e3-c08301fff1dd
Library Location
Natural and Mathematical Sciences
Date
2022-12-25
Notes
Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) ; Fundacao Araucaria de Apoio ao Desenvolvimento Cientifico e Tecnologico do Estado do Parana FA ; Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ)
Sample Text
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.
DOI
10.1016/j.jde.2022.09.015
Cilt
341
