Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

Name: Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation
Author: Bittencourt Moraes, G. E., Borluk, Handan, de Loreno, G., Muslu, G. M., Natali, F.

İsim	Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation
Yazar	Bittencourt Moraes, G. E., Borluk, Handan, de Loreno, G., Muslu, G. M., Natali, F.
Basım Tarihi:	2022-12-25
Basım Yeri	- Elsevier
Konu	Existence and uniqueness of minimizers, Fractional Schrödinger equation, Orbital stability, Small-amplitude periodic waves
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0022-0396
Kayıt Numarası	442df295-dd58-46e5-a0e3-c08301fff1dd
Lokasyon	Natural and Mathematical Sciences
Tarih	2022-12-25
Notlar	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)
Örnek Metin	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

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Kaynağa git

Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

Yazar Bittencourt Moraes, G. E., Borluk, Handan, de Loreno, G., Muslu, G. M., Natali, F.

Basım Tarihi 2022-12-25

Basım Yeri - Elsevier

Konu Existence and uniqueness of minimizers, Fractional Schrödinger equation, Orbital stability, Small-amplitude periodic waves

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0022-0396

Kayıt Numarası 442df295-dd58-46e5-a0e3-c08301fff1dd

Lokasyon Natural and Mathematical Sciences

Tarih 2022-12-25

Notlar 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)

Örnek Metin 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