Stable standing waves for a Schrödinger system with nonlinear<i>χ</i>3 response-Reference-Cited by-同舟云学术

Stable standing waves for a Schrödinger system with nonlinearχ3 response

Published:2023-10-01 Issue:10 Volume:64 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Colin Mathieu¹,Watanabe Tatsuya²^ORCID

Affiliation:

1. University of Bordeaux, CNRS, Bordeaux INP, IMB 1 , UMR 5251, F-33400 Talence, France

2. Department of Mathematics, Faculty of Science, Kyoto Sangyo University 2 , Motoyama, Kamigamo, Kita-ku, Kyoto-City 603-8555, Japan

Abstract

In this paper, we consider standing waves for a nonlinear Schrödinger system which appears in nonlinear optics. This two-component system contains a cubic nonlinear term which is called χ3-interaction, and has a strong coupling on one side only. Oliveira and Pastor [Anal. Math. Phys. 11, 123 (2021)] showed the existence of ground states solutions for the corresponding stationary problems and investigated their stability. In our study, by considering the solvability of a constraint minimization problem, we show the existence of stable standing wave solutions. We also investigate the correspondence between minimizers and ground state solutions.

Funder

Japan Society for the Promotion of Science

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0165615/18164384/101506_1_5.0165615.pdf

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