Multiple Breathers on a Vortex Filament

Salman, Hayder (2014) Multiple Breathers on a Vortex Filament. Journal of Physics: Conference Series, 544. ISSN 1742-6588

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Abstract

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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 31 Oct 2014 13:26
Last Modified: 22 Jul 2020 00:02
URI: https://ueaeprints.uea.ac.uk/id/eprint/50649
DOI: 10.1088/1742-6596/544/1/012005

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