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Title: Travelling solitary waves in lattice equations
Author: Melvin , Thomas R. O.
ISNI:       0000 0004 2677 9438
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2009
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This thesis is concerned with the existence and dynamics of travelling solitary waves in lattice equations, specifically a number of models of the discrete nonlinear Schrodinger equation (DNLS). The DNLS occurs in various forms when modelling a wide range of physical processes involving wave propagation. We provide a review of the literature and introduce some of the concepts that will be use to analyse the differential advance-delay equations which occur when posing lattice equations in a travelling frame. To show the existence of travelling solitary wave solutions to the DNLS three main methods are used, namely the pseudo-spectral method, Melnikov's method for the existence of homoclinic orbits and computation of the so-called Stokes constant for a beyond-all-orders asymptotic expansion. The pseudo-spectral method transforms the differential advance-delay equation into a large system of coupled algebraic equations which are solved numerically.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available