New connections between moving curves and soliton equations

Details New connections between moving curves and soliton equations New connections between moving curves and soliton equations

2001-04-27

arxiv.org/abs/nlin/0104066v2

Nonlinear Sciences

Pattern Formation and Solitons

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

Scientific paper

10.1016/S0375-9601(01)00632-6

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 Schr\"{o}dinger
equation is used to illustrate this explicitly.

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