Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy
Abstract
We provide a construction of the two-component Camassa-Holm (CH-2) hierarchy employing a new zero-curvature formalism and identify and describe in detail the isospectral set associated to all real-valued, smooth, and bounded algebro-geometric solutions of the th equation of the stationary CH-2 hierarchy as the real -dimensional torus . We employ Dubrovin-type equations for auxiliary divisors and certain aspects of direct and inverse spectral theory for self-adjoint singular Hamiltonian systems. In particular, we employ Weyl-Titchmarsh theory for singular (canonical) Hamiltonian systems. While we focus primarily on the case of stationary algebro-geometric CH-2 solutions, we note that the time-dependent case subordinates to the stationary one with respect to isospectral torus questions.
Keywords
Cite
@article{arxiv.1512.03956,
title = {Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy},
author = {Jonathan Eckhardt and Fritz Gesztesy and Helge Holden and Aleksey Kostenko and Gerald Teschl},
journal= {arXiv preprint arXiv:1512.03956},
year = {2017}
}
Comments
35 pages. arXiv admin note: substantial text overlap with arXiv:nlin/0208021