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

Gerald Teschl
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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.

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Gerald Teschl. 2006-12-04. Algebro-Geometric Constraints on Solitons with Respect to Quasi-Periodic Backgrounds. https://doi.org/10.1112/blms%2Fbdm038

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