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B. Kimia, A. Tannenbaum and S. Zucker, “On the Evolution of Curves via a Function of Curvature. I. The Classical Case,” Journal Mathematical Analysis and Application, Vol. 163, No. 2, 1992, pp. 438-458. doi:10.1016/0022-247X(92)90260-K

has been cited by the following article:

• TITLE: Computation of Some Geometric Properties for New Nonlinear PDE Models

  AUTHORS: Nassar Hassan Abdel-All, Mohammed Abdullah Abdullah Hamad, Mohammed Abdullah Abdel-Razek, Amal Aboelwafa Khalil

  KEYWORDS: Motion of Curve, Darboux Transformations, Gaussian and Mean Curvatures, Symmetry Groups

  JOURNAL NAME: Applied Mathematics, Vol.2 No.6, June 21, 2011

  ABSTRACT: The purpose of the present work is to construct new geometrical models for motion of plane curve by Darboux transformations. We get nonlinear partial differential equations (PDE). We have obtained the exact solutions of the resulting equations using symmetry groups method. Also, the Gaussian and mean curvatures of Monge form of the soliton surfaces have been calculated and discussed.