Solitons on moving space curves

Abstract

It is shown that the motion of certain types of helical space curves may be related to the sine–Gordon equation and to the Hirota equation (and consequently to the nonlinear Schrödinger equation and to the modified Korteweg–de Vries equation). The intrinsic equations that govern the motion of space curves are shown to provide the various linear equations that have been introduced to solve these evolution equations by inverse scattering methods.