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Title: Soliton equations in two spatial dimensions and their solutions
Author: Allami, Mohammed Jabbar Hawas
Awarding Body: University of Kent
Current Institution: University of Kent
Date of Award: 2011
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This thesis concerns soliton equations in two spatial dimensions. Camassa and Holm derived a model of shallow water wave which continues to attract attention in the light of the remarkable wealth of mathematical and physical properties of its solutions. More recently, Kraenkel and Zenchuk introduced an extension of Camassa and Holm's equation to two spatial dimensions, with three fields, and derived it from a Lax pair. However, finding solutions of this model is more challenging. In order to understand and find solutions of the (2 + l)-dimensional Camassa- Holm (CH) equation, it turns out that we have to study and analyse1ther soliton equations in two spatial dimensions, together with their hierarchies. To begin with, we consider a squared eigenfunction symmetry of the Kadomtsev-Petviashvili (KP) hierarchy, this results in a system of equations in (2 + 1)-dimensions. One of the main tools employed is Hirota's bilinear method. Using Hirota's per- turbation technique, one-, two- and three-soliton solutions of the KP squared eigen- function flow directly constructed, and numerical plots are presented. An ansatz for multisoliton solutions is proposed and proved by induction that it is correct. The soliton formula is shown to be equivalent to the formulae found by Freeman, Gilson and Nimmo, who derived Wronskian formulae for multisoliton solutions.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available