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Central affine curve flow on the plane

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Abstract

We give the following for Pinkall’s central affine curve flow on the plane: (i) a systematic and simple way to construct the known higher commuting curve flows, conservation laws, and a bi-Hamiltonian structure, (ii) Bäcklund transformations and a permutability formula, (iii) infinitely many families of explicit solutions. We also solve the Cauchy problem for periodic initial data.

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Correspondence to Chuu-Lian Terng.

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To Prof. Yvonne Choquet-Bruhat

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Terng, CL., Wu, Z. Central affine curve flow on the plane. J. Fixed Point Theory Appl. 14, 375–396 (2013). https://doi.org/10.1007/s11784-014-0161-8

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  • DOI: https://doi.org/10.1007/s11784-014-0161-8

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