Algebro‐geometric constraints on solitons with respect to quasi‐periodic backgrounds

@inproceedings{Teschl2007AlgebrogeometricCO,
  title={Algebro‐geometric constraints on solitons with respect to quasi‐periodic backgrounds},
  author={Gerald Teschl},
  year={2007}
}
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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