Central affine curve flow on the plane

• DOI: 10.1007/s11784-014-0161-8
• Publication Date: 2014-04-20T01:20:51Z
• Authors: Chuu-Lian Terng; Zhiwei Wu
• Keywords: Mathematics - Differential Geometry; Nonlinear Sciences - Exactly Solvable and Integrable Systems; Differential Geometry (math.DG); FOS: Mathematics; FOS: Physical sciences; 37K10, 37K30, 37K35, 53C44; Exactly Solvable and Integrable Systems (nlin.SI)

We give the following results 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) Baecklund transformations and a permutability formula, (iii) infinitely many families of explicit solutions. We also solve the Cauchy problem for periodic initial data.<br/>to appear in Journal of Fixed Point Theory and Applications (Choquet-Bruhat Festschrift)<br/>