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

Pages: 761 - 770, Issue Special, September 2009

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Suleyman Tek - Department of Computer Science, University of Arkansas at Little Rock, 2801 S. University Ave., Little Rock, AR 72204, United States (email)

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.

Keywords:  Soliton surfaces, Willmore surfaces, Weingarten surfaces, shape equa- tion, integrable equations
Mathematics Subject Classification:  Primary: 53A05, 53A35, 53C42, 35Q53, 35Q58; Secondary: 53C80, 35Q80

Received: July 2008;      Revised: February 2009;      Published: September 2009.