The Double Sine-Gordon Equations: A Physically Applicable System of Equations View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1980

AUTHORS

R. K. Bullough , P. J. Caudrey , H. M. Gibbs

ABSTRACT

We treat two physical problems--the propagation of ultra-short optical pulses in a resonant 5-fold degenerate medium, and the creation--and propagation of spin waves in the anisotropic magnetic liquids 3HeA and 3HeB at temperatures below the transition to the A phase at 2.6 mK. The optical pulse problem is governed by a ‘double’ sine-Gordon equation, the 3HeA problem by the sine-Gordon and the 3HeB by a double sine-Gordon with changed sign. The double sine-Gordons are not integrable: we study them analytically and numerically and predict a “wobbling” 4π pulse in the optical case, a result supported by experiments. We solve certain initial value problems and show how they could be used for the creation of spin excitations in 3HeA and 3HeB. Finally we develop singular perturbation theory in terms of sine-Gordon scattering data in order to describe the 4π wobbler and a similar 0π pulse. More... »

PAGES

107-141

Book

TITLE

Solitons

ISBN

978-3-642-81450-1
978-3-642-81448-8

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-81448-8_3

DOI

http://dx.doi.org/10.1007/978-3-642-81448-8_3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1021098252


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