Partial symmetry of normalized solutions for a doubly coupled Schrödinger system

Haijun Luo () and Zhitao Zhang ()
Additional contact information
Haijun Luo: Hunan University
Zhitao Zhang: The Chinese Academy of Sciences

Partial Differential Equations and Applications, 2020, vol. 1, issue 5, 1-15

Abstract: Abstract We consider the normalized solutions of a Schrödinger system which arises naturally from nonlinear optics, the Hartree–Fock theory for Bose–Einstein condensates. And we investigate the partial symmetry of normalized solutions to the system and their symmetry-breaking phenomena. More precisely, when the underlying domain is bounded and radially symmetric, we develop a kind of polarization inequality with weight to show that the first two components of the normalized solutions are foliated Schwarz symmetric with respect to the same point, while the latter two components are foliated Schwarz symmetric with respect to the antipodal point. Furthermore, by analyzing the singularly perturbed limit profiles of these normalized solutions, we prove that they are not radially symmetric at least for large nonlinear coupling constant $$\beta $$ β , which seems a new method to prove the symmetry-breaking phenomenons of normalized solutions.

Keywords: Schrödinger system; Normalized solution; Foliated Schwarz symmetry; Symmetry breaking; 35B06; 35J50; 35B09 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-020-00016-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:1:y:2020:i:5:d:10.1007_s42985-020-00016-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-020-00016-0

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().