The University of Southampton
University of Southampton Institutional Repository

Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime

Berry, M.V. and Dennis, M.R. (2001) Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime Journal of Physics A: Mathematical and General, 34, (42), pp. 8877-8888.

Record type: Article


As a parameter a is varied, the topology of nodal lines of complex scalar waves in space (i.e. their dislocations, phase singularities or vortices) can change according to a structurally stable reconnection process involving local hyperbolas whose branches switch. We exhibit families of exact solutions of the Helmholtz equation, representing knots and links that are destroyed by encounter with dislocation lines threading them when a is increased. In the analogous paraxial waves, the paraxial prohibition against dislocations with strength greater than unity introduces additional creation events. We carry out the analysis with polynomial waves, obtained by long-wavelength expansions of the wave equations. The paraxial events can alternatively be interpreted as knotting and linking of worldlines of dislocation points moving in the plane.

PDF JPA34_8877.pdf - Version of Record
Download (676kB)

More information

Published date: 2001
Organisations: Applied Mathematics


Local EPrints ID: 29379
ISSN: 0305-4470
PURE UUID: 758032f9-c978-43a6-bc60-e0f17bef8cde

Catalogue record

Date deposited: 12 May 2006
Last modified: 30 Sep 2017 04:56

Export record


Author: M.V. Berry
Author: M.R. Dennis

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.