New connections between moving curves and soliton equations

Abstract

Lamb has identified a certain class of moving space curves with soliton equations. We show that there are two other classes of curve evolution that may be so identified. Hence three distinct classes of curve evolution are associated with a given integrable equation. The nonlinear Schrödinger equation is used to illustrate this explicitly.

some minor corrections made. 17 pages. Accepted in Phys. Lett. A

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