Weingarten surfaces arising from soliton theory
Date
1999
Authors
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Gürses, Metin
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English
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Abstract
In this work we presented a method for constructing surfaces in associated with the symmetries of Gauss-Mainardi-Codazzi equations. We show that among these surfaces the sphere has a unique role. Under constant gauge transformations all integrable equations are mapped to a sphere. Furthermore we prove that all compact surfaces generated by symmetries of the sine-Gordon equation are homeomorphic to sphere. We also construct some Weingarten surfaces arising from the deformations of sine-Gordon, sinh-Gordon, nonlinear Schrödinger and modified Korteweg-de Vries equations.
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Mathematics
Degree Level
Master's
Degree Name
MS (Master of Science)