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

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


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