American Institute of Mathematical Sciences

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2009, 2009(Special): 761-770. doi: 10.3934/proc.2009.2009.761

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, United States

Received  July 2008 Revised  February 2009 Published  September 2009

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.
Keywords: Soliton surfaces, Weingarten surfaces, integrable equations, Willmore surfaces, shape equa- tion.
Mathematics Subject Classification: Primary: 53A05, 53A35, 53C42, 35Q53, 35Q58; Secondary: 53C80, 35Q80.
Citation: Suleyman Tek. Some classes of surfaces in $\mathbb{R}^3$ and $\M_3$ arising from soliton theory and a variational principle. Conference Publications, 2009, 2009 (Special) : 761-770. doi: 10.3934/proc.2009.2009.761
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