Algebro-Geometric Constraints on Solitons with Respect to Quasi-Periodic Backgrounds

Abstract

We investigate the algebraic conditions the scattering data of short-range perturbations of quasi-periodic finite-gap Jacobi operators have to satisfy. As our main result we provide the Poisson-Jensen-type formula for the transmission coefficient in terms of Abelian integrals on the underlying hyperelliptic Riemann surface and give an explicit condition for its single-valuedness. In addition, we establish trace formulas which relate the scattering data to the conserved quantities in this case.

9 pages. Bull. London Math. Soc. (to appear)

References in corpus (1)

• Scattering Theory for Jacobi Operators with Quasi-Periodic Background

Cited by in corpus (2)

• Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds Revisited
• Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds