Some distributional solutions of the CH, DP and CH2 equations and the Lax pair formalism
| dc.contributor.advisor | Szmigielski, Jacek | en_US |
| dc.contributor.committeeMember | Sowa, A. | en_US |
| dc.contributor.committeeMember | Smolyakov, Andrei I. | en_US |
| dc.contributor.committeeMember | Patrick, George W. | en_US |
| dc.contributor.committeeMember | Misiolek, G. | en_US |
| dc.creator | Mohajer, Keivan | en_US |
| dc.date.accessioned | 2008-09-16T13:21:21Z | en_US |
| dc.date.accessioned | 2013-01-04T04:58:40Z | |
| dc.date.available | 2009-09-18T08:00:00Z | en_US |
| dc.date.available | 2013-01-04T04:58:40Z | |
| dc.date.created | 2008-09 | en_US |
| dc.date.issued | 2008-09-01 | en_US |
| dc.date.submitted | September 2008 | en_US |
| dc.description.abstract | This 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.identifier.uri | http://hdl.handle.net/10388/etd-09162008-132121 | en_US |
| dc.language.iso | en_US | en_US |
| dc.subject | peakons | en_US |
| dc.subject | distributional solutions | en_US |
| dc.subject | Lax pair | en_US |
| dc.title | Some distributional solutions of the CH, DP and CH2 equations and the Lax pair formalism | en_US |
| dc.type.genre | Thesis | en_US |
| dc.type.material | text | en_US |
| thesis.degree.department | Mathematics and Statistics | en_US |
| thesis.degree.discipline | Mathematics and Statistics | en_US |
| thesis.degree.grantor | University of Saskatchewan | en_US |
| thesis.degree.level | Doctoral | en_US |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) | en_US |