Geometry of Evolving Plane Curves Problem via Lie Group Analysis

Abstract

The purpose of the present work is to construct new geometrical models for motion of plane curves. We have obtained nonlinear partial differential equations and have discussed the solutions of these equations using symmetry groups methods. Also, geometric interpretation for these solutions are given through the Gaussian and mean curvatures to the soliton surfaces attached to the solution of the evolving problem. Key Words: Motion of curve; Symmetry groups; Monge form