| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 79 | |
| Number of page(s) | 31 | |
| DOI | https://doi.org/10.1051/cocv/2024065 | |
| Published online | 07 October 2024 | |
Variational properties of space-periodic standing waves of nonlinear Schrödinger equations with general nonlinearities
1
Institut de Mathématiques de Toulouse; UMR5219, Université de Toulouse; CNRS, INSA IMT, 31077 Toulouse, France
2
Present address: American University in Dubai, Dubai, United Arab Emirates
3
Institut de Mathématiques de Toulouse; UMR5219, Université de Toulouse; CNRS, UPS IMT, 31062 Toulouse Cedex 9, France
* Corresponding author: perlakf1@gmail.com
Received:
3
May
2024
Accepted:
24
August
2024
Periodic waves are standing wave solutions of nonlinear Schrödinger equations whose profile is periodic in space dimension one. We consider general nonlinearities and provide variational characterizations for the periodic wave profiles. This involves minimizing energy while keeping mass and momentum constant, as well as minimizing the action over the Nehari manifold. These variational approaches are considered both in the periodic and anti-periodic settings, and for focusing and defocusing nonlinearities. In appendix, we study the existence properties of periodic solutions of the triple power nonlinearity.
Mathematics Subject Classification: 35Q55 / 35B10 / 35A15
Key words: Nonlinear Schrödinger equation / standing waves / Nehari manifold / normalized solutions / variational method / periodic solutions
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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