Some classes of surfaces in $\mathbb{R}^3$ and $\M_3$ arising from soliton theory and a variational principle

Suleyman Tek

doi:10.3934/proc.2009.2009.761

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2009, Volume 2009: 761-770. Doi: 10.3934/proc.2009.2009.761 open access

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Some classes of surfaces in $\mathbb{R}^3$ and $\M_3$ arising from soliton theory and a variational principle

Suleyman Tek^1,

1.
Department of Computer Science, University of Arkansas at Little Rock, 2801 S. University Ave., Little Rock, AR 72204

Received: June 30, 2008

Revised: January 31, 2009

Published: August 2009

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Abstract

In this paper, modified Korteweg-de Vries (mKdV) and Harry Dym (HD) surfaces are considered which are arisen from using soliton surface technique and a variational principle. Some of these surfaces belong to Willmore-like and Weingarten surfaces, and surfaces that solve the generalized shape equation classes. Moreover, parameterized form of these surfaces are found for given solutions of the mKdV and HD equations.

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Mathematics Subject Classification: Primary: 53A05, 53A35, 53C42, 35Q53, 35Q58; Secondary: 53C80, 35Q80.

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