Lagrangian time-discretization of the Hunter-Saxton equation
arXiv:math-ph/0201035 · doi:10.1016/S0375-9601(02)01388-9
Abstract
We study Lagrangian time-discretizations of the Hunter-Saxton equation. Using the Moser-Veselov approach, we obtain such discretizations defined on the Virasoro group and on the group of orientation-preserving diffeomorphisms of the circle. We conjecture that one of these discretizations is integrable.
13 pages, LaTeX, no figures. Version 2: New section about the group of orientation-preserving diffeomorphisms of the circle is added. Version 3: Minor changes, bibliography updated. Version 4: Corrected typos