Reconstruction of the Transmission Coefficient for Steplike Finite-gap Backgrounds
نویسنده
چکیده
We consider scattering theory for one-dimensional Jacobi operators with respect to steplike quasi-periodic finite-gap backgrounds and show how the transmission coefficient can be reconstructed from minimal scattering data. This generalizes the Poisson–Jensen formula for the classical constant background case.
منابع مشابه
On the Cauchy Problem for the Korteweg–de Vries Equation with Steplike Finite-Gap Initial Data II. Perturbations with Finite Moments
We solve the Cauchy problem for the Korteweg–de Vries equation with steplike finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite.
متن کاملOn the Cauchy Problem for the Modified Korteweg–de Vries Equation with Steplike Finite-Gap Initial Data
We solve the Cauchy problem for the modified Korteweg–de Vries equation with steplike quasi-periodic, finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite.
متن کاملInverse Scattering Theory for One-dimensional Schrödinger Operators with Steplike Finite-gap Potentials
We develop direct and inverse scattering theory for one-dimensional Schrödinger operators with steplike potentials which are asymptotically close to different finite-gap potentials on different half-axes. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.
متن کاملInverse Scattering Theory for One-dimensional Schrödinger Operators with Steplike Periodic Potentials
We develop direct and inverse scattering theory for one-dimensional Schrödinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.
متن کاملAlgebro-geometric Constraints on Solitons with Respect to Quasi-periodic Backgrounds
We investigate the algebraic conditions that have to be satisfied by the scattering data of short-range perturbations of quasi-periodic finite-gap Jacobi operators in order to allow solvability of the inverse scattering problem. Our main result provides a Poisson-Jensen-type formula for the transmission coefficient in terms of Abelian integrals on the underlying hyperelliptic Riemann surface an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008