Standing waves for a Schrödinger system with three waves interaction

[2210.07643] Standing waves for a Schrödinger system with three waves interaction Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2210.07643 (math) [Submitted on 14 Oct 2022 ( v1 ), last revised 15 Apr 2026 (this version, v2)] Title: Standing waves for a Schrödinger system with three waves interaction Authors: Luigi Forcella , Xiao Luo , Tao Yang , Xiaolong Yang View a PDF of the paper titled Standing waves for a Schr\"odinger system with three waves interaction, by Luigi Forcella and 3 other authors View PDF HTML (experimental) Abstract: We study standing waves for a system of nonlinear Schrödinger equations with three waves interaction arising as a model for the Raman amplification in a plasma. We consider the mass-critical and mass-supercritical regimes, and we prove existence of ground states along with a synchronized mass collapse behavior. In addition, we show that the set of ground states is stable under the associated Cauchy flow. Furthermore, in the mass-supercritical setting we construct an excited state that corresponds to a strongly unstable standing wave. Moreover, a semi-trivial limiting behavior of the excited state is drawn accurately. Finally, by a refined control of the excited state's energy, we give sufficient conditions to prove global existence or blow-up of solutions to the corresponding Cauchy problem. Comments: revised version. slightly shortened, typos fixed Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:2210.07643 [math.AP] (or arXiv:2210.07643v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2210.07643 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Math. Ann. (2026) Related DOI : https://doi.org/10.1007/s00208-026-03380-1 Focus to learn more DOI(s) linking to related resources Submission history From: Luigi Forcella [ view email ] [v1] Fri, 14 Oct 2022 08:51:12 UTC (34 KB) [v2] Wed, 15 Apr 2026 08:12:44 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled Standing waves for a Schr\"odinger system with three waves interaction, by Luigi Forcella and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2022-10 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger equations#617916
• Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger equations#617416
• Three Degree of Freedom Wave Energy Converter Design for Resonant Motion#173972
• Soliton Dynamics for the Cubic-Quintic Nonlinear Schrödinger Equation with a Potential#1061284
• Three-dimensional hybrid asynchronous perfectly matched layer for wave propagation in heterogeneous semi-infinite media#417922