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- W3092276618 abstract "Twenty five years ago U. Pinkall discovered that the Korteweg-de Vries equation can be realized as an evolution of curves in centroaffine geometry. Since then, a number of authors interpreted various properties of KdV and its generalizations in terms of centroaffine geometry. In particular, the Bäcklund transformation of the Korteweg-de Vries equation can be viewed as a relation between centroaffine curves. Our paper concerns self-Bäcklund centroaffine curves. We describe general properties of these curves and provide a detailed description of them in terms of elliptic functions. Our work is a centroaffine counterpart to the study done by F. Wegner of a similar problem in Euclidean geometry, related to Ulam’s problem of describing the (2-dimensional) bodies that float in equilibrium in all positions and to bicycle kinematics. We also consider a discretization of the problem where curves are replaced by polygons. This is related to discretization of KdV and the cross-ratio dynamics on ideal polygons." @default.
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- W3092276618 date "2022-08-24" @default.
- W3092276618 modified "2023-09-27" @default.
- W3092276618 title "Self-Bäcklund curves in centroaffine geometry and Lamé’s equation" @default.
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- W3092276618 doi "https://doi.org/10.1090/cams/9" @default.
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