Scaling invariance of helical curve motion and soliton equations

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Abstract
The scaling properties of the equations describing the motion of helical curves determine the scaling of the associated nonlinear evolution equations. Only two polynomial scaling‐invariant evolution equations can be found. Of these, the nonlinear Schrödinger equation has the physically correct scaling invariance, but the modified Korteweg–de Vries can not be connected to realistic helical curves.