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dc.contributor.advisorMueller, Jennifer
dc.contributor.authorCroke, Ryan P.
dc.contributor.committeememberBradley, Mark
dc.contributor.committeememberShipman, Patrick
dc.contributor.committeememberZhou, Yongcheng
dc.date.accessioned2007-01-03T08:09:45Z
dc.date.available2007-01-03T08:09:45Z
dc.date.issued2012
dc.description2012 Spring.
dc.descriptionIncludes bibliographical references.
dc.description.abstractIntegrable systems in two spatial dimensions have received far less attention by scholars than their one--dimensional counterparts. In this dissertation the Novikov--Veselov (NV) equation, a (2+1)--dimensional integrable system that is a generalization of the famous Korteweg de--Vreis (KdV) equation is investigated. New traveling wave solutions to the NV equation are presented along with an analysis of the stability of certain types of soliton solutions to transverse perturbations. To facilitate the investigation of the qualitative nature of various types of solutions, including solitons and their stability under transverse perturbations, a version of a pseudo-spectral numerical method introduced by Feng [J. Comput. Phys., 153(2), 1999] is developed. With this fast numerical solver some conjectures related to the inverse scattering method for the NV equation are also examined. The scattering transform for the NV equation is the same as the scattering transform used to solve the inverse conductivity problem, a problem useful in medical applications and seismic imaging. However, recent developments have shed light on the nature of the long-term behavior of certain types of solutions to the NV equation that cannot be investigated using the inverse scattering method. The numerical method developed here is used to research these exciting new developments.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierCroke_colostate_0053A_11099.pdf
dc.identifierETDF2012400230MATH
dc.identifier.urihttp://hdl.handle.net/10217/67426
dc.languageEnglish
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019 - CSU Theses and Dissertations
dc.rightsCopyright of the original work is retained by the author.
dc.titleInvestigation of the Novikov-Veselov equation: new solutions, stability and implications for the inverse scattering transform, An
dc.typeText
dcterms.rights.dplaThe copyright and related rights status of this Item has not been evaluated (https://rightsstatements.org/vocab/CNE/1.0/). Please refer to the organization that has made the Item available for more information.
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)


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