论文信息 - Integrable geometric evolution equations for curves

Integrable geometric evolution equations for curves

The vortex filament flow and planar filament flow are examples of evolution equations which commute with Euclidean isometries and are also integrable, in that they induce completely integrable PDE for curvature—the focusing nonlinear Schodinger equation and the mKdV equations, respectively. In this note we outline an approach for classifying integrable geometric evolution equations for planar curves, using necessary conditions derived by Mikhailov et al, based on generalized symmetries of arbitrarily high order. Here we give new examples of integrable third-order curve flows obtained by this classification, and discuss their conservation laws, recursion operators, and related flows for curves in R3.

T. Ivey

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