Central affine curve flow on the plane |
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| Authors: | Chuu-Lian Terng Zhiwei Wu |
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| Affiliation: | 1. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697-3875, USA
2. Department of Mathematics, Ningbo University, Ningbo, Zhejiang, 315211, China
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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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