2018
DOI: 10.14495/jsiaml.10.25
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Defocusing mKdV flow on centroaffine plane curves

Abstract: We show that plane curves in the centroaffine geometry admit a flow which is described by the defocusing modified KdV equation. We establish a correspondence between this flow and the KdV flow in the equicentroaffine geometry. We also present an explicit formula for the KdV flow in terms of the τ function.

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“…For example, the KdV equation describes a motion of plane curves that preserves the areal velocity [9]. Moreover, in recent years, explicit formulas for these curve motions have been established in [10,11,12,13] by using the theory of τ functions.…”
Section: Introductionmentioning
confidence: 99%
“…For example, the KdV equation describes a motion of plane curves that preserves the areal velocity [9]. Moreover, in recent years, explicit formulas for these curve motions have been established in [10,11,12,13] by using the theory of τ functions.…”
Section: Introductionmentioning
confidence: 99%