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

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

2006-06-26

arxiv.org/abs/nlin/0606062v3

Bull. London Math. Soc. 39-4, 677-684 (2007)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1112/blms/bdm038

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.

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