Algebro-Geometric Solutions of the Sine-Gordon Hierarchy

Abstract On the basis of two sets Lenard recursion sequences and zero-curvature equation associated with a matrix spectral problem, we derive entire sine-Gordon hierarchy, which is composed all positive negative flows. Using theory hyperelliptic curves, Abel-Jacobi coordinates are introduced, from corresponding flows linearized. The algebro-geometric solutions hierarchy constructed by using asymptotic properties meromorphic function.