Multiple breathers on a vortex filament

Tangled Magnetic Fields in Astro- and Plasma Physics; Quantised Flux in Tightly Knotted and Linked Systems

Salman, H.^1

School of Mathematics, University of East Anglia, Norwich Research Park, Norwich

NR4 7TJ, United Kingdom^1

关键词: Dinger equation;    Helical vortices;    Homoclinic;    Local induction approximations;    Self focussing;    Three-dimensional motion;    Vortex configurations;    Vortex filament;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/544/1/012005/pdf
DOI  :  10.1088/1742-6596/544/1/012005

来源: IOP

【 摘 要 】

In this paper we investigate the correspondence between the Da Rios-Betchov equation, which appears in the three-dimensional motion of a vortex filament, and the nonlinear Schrödinger equation. Using this correspondence we map a set of solutions corresponding to breathers in the nonlinear Schrödinger equation to waves propagating along a vortex filament. The work presented generalizes the recently derived family of vortex configurations associated with these breather solutions to a wider class of configurations that are associated with combination homoclinic/heteroclinic orbits of the 1D self-focussing nonlinear Schrödinger equation. We show that by considering these solutions of the governing nonlinear Schrödinger equation, highly nontrivial vortex filament configurations can be obtained that are associated with a pair of breather excitations. These configurations can lead to loop-like excitations emerging from an otherwise weakly perturbed helical vortex. The results presented further demonstrate the rich class of solutions that are supported by the Da Rios-Betchov equation that is recovered within the local induction approximation for the motion of a vortex filament.