Weingarten surfaces arising from soliton theory

Date

1999

Editor(s)

Advisor

Gürses, Metin

Supervisor

Co-Advisor

Co-Supervisor

Instructor

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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.

Source Title

Publisher

Course

Other identifiers

Book Title

Degree Discipline

Mathematics

Degree Level

Master's

Degree Name

MS (Master of Science)

Citation

Published Version (Please cite this version)

Language

English

Type