Motion of Curves on Two Dimensional Surfaces and Soliton Equations

Abstract

A connection is established between the soliton equations and curves moving in a three dimensional space $V_3$. The sign of the self-interacting terms of the soliton equations are related to the signature of $V_3$. It is shown that there corresponds a moving curve to each soliton equations.

arXiv commentLatex, 15 pp, to be published in Physics Letters A

References in corpus (1)

• Variable Coefficient Third Order KdV Type of Equations

Cited by in corpus (4)

• Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces
• Symplectically-invariant soliton equations from non-stretching geometric curve flows
• A Lie algebra structure on variation vector fields along curves in $2$-dimensional space forms
• Integrability of a nonlinear evolution equation derived from isoperimetric plane curve motion