Geometrical interpretations of Bäcklund transformations and certain types of partial differential equations : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University
dc.contributor.author | Selvaratnam, Anton Raviraj | |
dc.date.accessioned | 2018-01-11T20:43:54Z | |
dc.date.available | 2018-01-11T20:43:54Z | |
dc.date.issued | 2000 | |
dc.description | Page 37 is missing from the original copy. | en_US |
dc.description.abstract | Gauss' Theorema Egregium contains a partial differential equation relating the Gaussian curvature K to components of the metric tensor and its derivatives. Well known partial differential equations such as the Schrödinger equation and the sine-Gordon equation correspond to this PDE for special choices of K and special coördinate systems. The sine-Gordon equation, for example, can be derived via Gauss' equation for K = –1 using the Tchebychef net as a coördinate system. In this thesis we consider a special class of Bäcklund Transformations which correspond to coördinate transformations on surfaces having a specified Gaussian curvature. These transformations lead to Gauss' PDE in different forms and provide a method for solving certain classes of non-linear second order partial differential equations. In addition, we develop a more systematic way to obtain a coordinate system for a more general class of PDE, such that this PDE corresponds to the Gauss equation. | en_US |
dc.identifier.uri | http://hdl.handle.net/10179/12540 | |
dc.language.iso | en | en_US |
dc.publisher | Massey University | en_US |
dc.rights | The Author | en_US |
dc.subject | Partial Differential Equations | en_US |
dc.subject | Bäcklund transformations | en_US |
dc.title | Geometrical interpretations of Bäcklund transformations and certain types of partial differential equations : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University | en_US |
dc.type | Thesis | en_US |
massey.contributor.author | Selvaratnam, Anton Raviraj | |
thesis.degree.discipline | Mathematics | en_US |
thesis.degree.grantor | Massey University | en_US |
thesis.degree.level | Masters | en_US |
thesis.degree.name | Master of Science (M. Sc.) | en_US |
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