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Steady solutions for the Schrödinger map equation

2023/02/07 by Claudia García, Luis Vega, García, Claudia +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2302.03564

openalex publication_date 2023/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

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