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dc.contributor.advisorSzmigielski, Jaceken_US
dc.creatorMohajer, Keivanen_US
dc.date.accessioned2008-09-16T13:21:21Zen_US
dc.date.accessioned2013-01-04T04:58:40Z
dc.date.available2009-09-18T08:00:00Zen_US
dc.date.available2013-01-04T04:58:40Z
dc.date.created2008-09en_US
dc.date.issued2008-09-01en_US
dc.date.submittedSeptember 2008en_US
dc.identifier.urihttp://hdl.handle.net/10388/etd-09162008-132121en_US
dc.description.abstractThis dissertation deals with a class of nonlinear wave equations of the type discovered by R. Camassa and D. D. Holm which includes the Camassa-Holm, the Degasperis-Procesi, and the two component Camassa-Holm equations. All these equations admit certain non-smooth soliton-like solutions, called peakons as well as other non-smooth solutions like cuspons. We apply the techniques of the theory of distributions of L. Schwartz to study these solutions. In particular, every non-smooth traveling wave which is a distributional solution of the two component Camassa-Holm equation is a distributional solution of the Camassa-Holm equation if the set of points where the height of the wave equals its speed, is of measure zero. This includes peakon or cuspon traveling wave solutions.We also develop a suitable modification of the classical Lax pair formalism to deal with singular solutions. We show that the Lax pair formalism can be extended to a distributional weak Lax pair which is appropriate for dealing with the peakon solutions of the Camassa-Holm equation.en_US
dc.language.isoen_USen_US
dc.subjectpeakonsen_US
dc.subjectdistributional solutionsen_US
dc.subjectLax pairen_US
dc.titleSome distributional solutions of the CH, DP and CH2 equations and the Lax pair formalismen_US
thesis.degree.departmentMathematics and Statisticsen_US
thesis.degree.disciplineMathematics and Statisticsen_US
thesis.degree.grantorUniversity of Saskatchewanen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US
dc.type.materialtexten_US
dc.type.genreThesisen_US
dc.contributor.committeeMemberSowa, A.en_US
dc.contributor.committeeMemberSmolyakov, Andrei I.en_US
dc.contributor.committeeMemberPatrick, George W.en_US
dc.contributor.committeeMemberMisiolek, G.en_US


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