An alternative approach to the quasiPeriodic solutions of the HunterSaxton hierarchy
Abstract
This paper is dedicated to provide the global solutions of algebrogeometric type for all the equations of a new commuting hierarchy containing the HunterSaxton (HS) equation. Our main tools include the zero curvature method to derive the HS hierarchy, the generalized Jacobian variety, the generalized Riemann theta function, the Weyl $m$fucntions $m_\pm(x,t,z)$, and the pole motion obtained by solving an inverse problem for the SturmLiouville equation $L(\psi_1)=\psi_1^{\prime\prime}=zy\psi_1$. Based on these tools and the theory of nonautonomous differential systems, topological dynamics and ergodic theory, the algebrogeometric solutions are obtained for the entire HS hierarchy.
 Publication:

arXiv eprints
 Pub Date:
 January 2013
 DOI:
 10.48550/arXiv.1301.0690
 arXiv:
 arXiv:1301.0690
 Bibcode:
 2013arXiv1301.0690Y
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 37 pages