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Steady solutions for the Schrödinger map equation

Name: Steady solutions for the Schrödinger map equation
Keywords: Mathematics - Analysis of PDEs, FOS: Mathematics, Analysis of PDEs (math.AP)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 02 Jun 2024Embargo end date: 01 Jan 2023Publisher:Informa UK LimitedJournal:Communications in Partial Differential Equations, volume 49, pages 505-542 (issn: 0360-5302, eissn: 1532-4133,

Authors: Claudia García; Luis Vega;

doi: 10.1080/03605302.2024.2358500 , 10.48550/arxiv.2302.03564

arXiv: http://arxiv.org/abs/2302.03564

Steady solutions for the Schrödinger map equation

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Abstract

In this paper we use bifurcation methods to construct a new family of solutions of the binormal flow, also known as the vortex filament equation, which do not change their form. Our examples are complementary to those obtained by S. Kida in 1981, and therefore they are also related, thanks to the so-called Hasimoto transformation, to travelling wave solutions of the 1d cubic non-linear Schrödinger equation.

Related Organizations

University of the Basque Country
Spain
University of Granada
Spain

Keywords

Mathematics - Analysis of PDEs, FOS: Mathematics, Analysis of PDEs (math.AP)

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