{"id":{"repo_id":"carleton","oai_identifier":"oai:carleton.scholaris.ca:20.500.14718/40153"},"canonical_url":"https://search.dev.ndltd.org/etd/carleton/oai:carleton.scholaris.ca:20.500.14718/40153","repository":{"repo_id":"carleton","name":"Carleton University","base_url":"https://carleton.scholaris.ca/server/oai/request"},"display":{"title":"Asymptotic Analysis of Perturbations to Travelling Wave Solutions of Nonlinear Advection-Reaction-Diffusion Equations of Fisher Type","abstract":"In this thesis we examine some nonlinear advection-diffusion-reaction equations of Fisher type. First we discuss the stability properties of the equations by writing each nonlinear equation as a system of two ordinary different equations and then analyzing the stability of their equilibrium solutions and plotting their trajectories in phase portraits. We then describe the derivation of some exact expressions for travelling wave solutions which had been obtained by previous researcher using other methods. We examine some situations where the exact travelling wave solutions are perturbed. First we perturb the initial condition and then derive approximate expressions for the perturbations. The goal of the thesis is to investigate the case where the constant speed of the background medium is perturbed by a small-amplitude spatially and temporally localized perturbation.","abstract_html":"In this thesis we examine some nonlinear advection-diffusion-reaction equations of Fisher type. First we discuss the stability properties of the equations by writing each nonlinear equation as a system of two ordinary different equations and then analyzing the stability of their equilibrium solutions and plotting their trajectories in phase portraits. We then describe the derivation of some exact expressions for travelling wave solutions which had been obtained by previous researcher using other methods. We examine some situations where the exact travelling wave solutions are perturbed. First we perturb the initial condition and then derive approximate expressions for the perturbations. The goal of the thesis is to investigate the case where the constant speed of the background medium is perturbed by a small-amplitude spatially and temporally localized perturbation.","abstract_has_math":false,"creators":["Alruwaele, Wasaif"],"institution":"Carleton University","degree_name":"Master of Science (M.Sc.)","degree_level":"Master's","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-24T01:34:45Z","subjects":[],"languages":["en"],"rights":["Copyright © 2017 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. 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Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.22215/etd/2017-11855"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/20.500.14718/40153"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we examine some nonlinear advection-diffusion-reaction equations of Fisher type. First we discuss the stability properties of the equations by writing each nonlinear equation as a system of two ordinary different equations and then analyzing the stability of their equilibrium solutions and plotting their trajectories in phase portraits. We then describe the derivation of some exact expressions for travelling wave solutions which had been obtained by previous researcher using other methods. We examine some situations where the exact travelling wave solutions are perturbed. First we perturb the initial condition and then derive approximate expressions for the perturbations. The goal of the thesis is to investigate the case where the constant speed of the background medium is perturbed by a small-amplitude spatially and temporally localized perturbation."]},{"key":"dc:title","label":"Title","values":["Asymptotic Analysis of Perturbations to Travelling Wave Solutions of Nonlinear Advection-Reaction-Diffusion Equations of Fisher Type"]}]}],"canonical_facts":{"dc:creator":["Alruwaele, Wasaif"],"dc:date.accessioned":["2025-04-08T19:55:11Z"],"dc:date.available":["2025-04-08T19:55:11Z"],"dc:date.issued":["2017"],"dc:description.abstract":["In this thesis we examine some nonlinear advection-diffusion-reaction equations of Fisher type. First we discuss the stability properties of the equations by writing each nonlinear equation as a system of two ordinary different equations and then analyzing the stability of their equilibrium solutions and plotting their trajectories in phase portraits. We then describe the derivation of some exact expressions for travelling wave solutions which had been obtained by previous researcher using other methods. We examine some situations where the exact travelling wave solutions are perturbed. First we perturb the initial condition and then derive approximate expressions for the perturbations. The goal of the thesis is to investigate the case where the constant speed of the background medium is perturbed by a small-amplitude spatially and temporally localized perturbation."],"dc:identifier.doi":["10.22215/etd/2017-11855"],"dc:identifier.uri":["https://hdl.handle.net/20.500.14718/40153"],"dc:language.iso":["en"],"dc:publisher":["Carleton University"],"dc:rights":["Copyright © 2017 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. 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