In this work we use the Zakharov-Kuznetsov equation to study the evolution of a plane soliton subjected to a two-dimensional perturbation. The first part of the thesis is concerned with determining the growth rate of such a perturbation. We present two closely related methods which allow us to obtain rigorously the growth rates much more directly and simply than previous approaches. Both methods are general and hence applicable to other problems. If the perturbation is of a large enough wavelength, the plane soliton will evolve into more stable coherent structures of the form of two-dimensional solitons. This process is the subject of the remainder of the thesis. A weakly nonlinear analysis which fully describes the preliminary stages of the process is developed. We have studied how the eventual fate of a plane soliton is affected by the wavelength of the perturbation and obtained a simple formula for the variation of the number of cylindrical solitons formed with this wavelength. The methods developed in this thesis have been used to obtain an analytical description of a soliton state that occurs in coupled optical fibres.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:283476 |
| Date | January 1994 |
| Creators | Allen, Michael A. |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/107575/ |
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