Motion of Curves and Solitons
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A large class of physical, chemical, and biological systems can be modeled in terms of their contour dynamics, namely the kinematics and dynamics of their boundaries [329, 248, 249]. In many situations (e.g., when the inside bulk has the property of being “incompressible”) such contour representations are the most natural, and are simpler ones. Basically, the contour dynamics approach reduces the problem to the study of motion of curves and surfaces, especially the closed ones. In this chapter, we focus on the analysis of the motion of curves in the three-dimensional Euclidean space.