Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.503947
Title: Travelling solitary waves in lattice equations
Author: Melvin , Thomas R. O.
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2009
Availability of Full Text:
Access through EThOS:
Abstract:
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: uk.bl.ethos.503947  DOI: Not available
Share: