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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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