Scattering Operators for Matrix Zakharov-Shabat Systems

نویسندگان

  • Francesco Demontis
  • Cornelis van der Mee
چکیده

In this article the scattering matrix pertaining to the defocusing matrix Zakharov-Shabat system on the line is related to the scattering operator arising from time-dependent scattering theory. Further, the scattering data allowing for a unique retrieval of the potential in the defocusing matrix Zakharov-Shabat system are characterized. Mathematics Subject Classification (2000). Primary 34A55, 81U20; Secondary 81U40.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Wave Operators for Defocusing Matrix Zakharov-shabat Systems with Potentials Nonvanishing at Infinity

In this article we prove that the wave operators describing the direct scattering of the defocusing matrix Zakharov-Shabat system with potentials having distinct nonzero values with the same modulus at ±∞ exist, are asymptotically complete, and lead to a unitary scattering operator. We also prove that the free Hamiltonian operator is absolutely continuous.

متن کامل

Marchenko Equations and Norming Constants of the Matrix Zakharov–shabat System

In this article we derive the Marchenko integral equations for solving the inverse scattering problem for the matrix Zakharov-Shabat system with a potential without symmetry properties and having L1 entries under a technical hypothesis preventing the accumulation of discrete eigenvalues on the continuous spectrum. Wederive additional symmetry properties in the focusing case. The norming constan...

متن کامل

Time-evolution-proof Scattering Data for the Focusing and Defocusing Zakharov-Shabat Systems

Nonlinear Schrödinger (NLS) equations have attracted the attention of the physical and mathematical community for over four decades. NLS equations arise in such diverse fields as deep water waves [4, 25], plasma physics [24], fiber optics [11], and Bose-Einstein condensation [17]. The basic method for solving the NLS initial-value problem is the inverse scattering transform (IST) method [2–4, 6...

متن کامل

An Alternative Approach to Integrable Discrete Nonlinear Schrödinger Equations

In this article we develop the direct and inverse scattering theory of a discrete matrix Zakharov-Shabat system with solutions Un and W n. Contrary to the discretization scheme enacted by Ablowitz and Ladik, a central difference scheme is applied to the positional derivative term in the matrix Zakharov-Shabat system to arrive at a different discrete linear system. The major effect of the new di...

متن کامل

Wave operators for the matrix Zakharov–Shabat system

In this article, we prove the similarity and, in the focusing case, the J-unitary equivalence of the free Hamiltonian and the restriction of the full Hamiltonian to the maximal invariant subspace on which its spectrum is real for the matrix Zakharov–Shabat system under suitable conditions on the potentials. This restriction of the full Hamiltonian is shown to be a scalar-type spectral operator ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008