Steady solutions for the Schr\"odinger map equation
Analysis of PDEs
2023-02-08 v1
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 Schr\"odinger equation.
Keywords
Cite
@article{arxiv.2302.03564,
title = {Steady solutions for the Schr\"odinger map equation},
author = {Claudia García and Luis Vega},
journal= {arXiv preprint arXiv:2302.03564},
year = {2023}
}