City Research Online

Abstract

The reasons for creating a nonlinear field theory of fundamental particles are advanced. The foundations of electrodynamics are discussed with especial regard to the difficulties which arise with elementary charges. The nonlinear field theory of Born and Infeld is reviewed.

The methods of solving soliton equations are presented. The multisoliton of many nonlinear partial differential equations are summarised.

The attempts to treat solitons as particles in interaction are reviewed including the Bowtell-Stuart analysis of soliton interactions in terms of the singularities of the complex multisoliton solution.

The concepts of nonlinear and linear superposition of solitons are presented.

The author derives, by an original technique the multisoliton solution of the sG (solitons, antisolitons and breathers) using the theorem of permutability. The multisoliton solution is shown explicitly to decompose into a collection of solitons, antisolitons and breathers in the asymptotic limits of time.

The author proposes a new linear superposition principle for the multisoliton solutions of many equations. With this new principle the solitons are identified throughout the multisoliton interaction and the soliton interaction is analysed. The soliton positions (taken to be the projections on the real axis of the singularities of the complex multisoliton solution) are found to be related to the roots of a polynomial of degree N. In addtion to providing a means of understanding soliton interaction, the new linear superposition principle of the author leads to remarkable connections between the multisoliton solutions of many equations. It also allows the author to find clse global approximations to the multisoliton solutions.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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