An alternative approach to the quasi-Periodic solutions of the Hunter-Saxton hierarchy

Abstract

This paper is dedicated to provide the global solutions of algebro-geometric type for all the equations of a new commuting hierarchy containing the Hunter-Saxton (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 Sturm-Liouville 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 algebro-geometric solutions are obtained for the entire HS hierarchy.

37 pages

References in corpus (2)

• On a Whitham-Type Equation
• Contact Equivalence of the Generalized Hunter - Saxton Equation and the Euler - Poisson Equation