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

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dc.contributor.authorSelvaratnam, Anton Raviraj
dc.date.accessioned2018-01-11T20:43:54Z
dc.date.available2018-01-11T20:43:54Z
dc.date.issued2000
dc.descriptionPage 37 is missing from the original copy.en_US
dc.description.abstractGauss' 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.urihttp://hdl.handle.net/10179/12540
dc.language.isoenen_US
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectPartial Differential Equationsen_US
dc.subjectBäcklund transformationsen_US
dc.titleGeometrical 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 Universityen_US
dc.typeThesisen_US
massey.contributor.authorSelvaratnam, Anton Raviraj
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Science (M. Sc.)en_US
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