Stable standing waves for a Schrödinger system with nonlinear χ 3 response

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)]...

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Bibliographic Details
Published in:Journal of mathematical physics 2023-10, Vol.64 (10)
Main Authors: Colin, Mathieu, Watanabe, Tatsuya
Format: Article
Language:English
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0165615