Scattering data computation for the Zakharov-Shabat system
نویسندگان
چکیده
منابع مشابه
Scattering Operators for Matrix Zakharov-Shabat Systems
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, ...
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The dressing procedure for the Generalised Zakharov-Shabat system is well known for systems, related to sl(N) algebras. We extend the method, constructing explicitly the dressing factors for some systems, related to orthogonal and symplectic Lie algebras. We consider ’dressed’ fundamental analytical solutions with simple poles at the prescribed eigenvalue points and obtain the corresponding Lax...
متن کاملTime-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...
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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 ...
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For various spaces of potentials we prove that the set of finite gap potentials of the ZakharovShabat system is dense. In particular our result holds for Sobolev spaces and for spaces of analytic potentials of a given type. Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-21875 Originally published at: Grébert, B; Kappeler, T (2003). D...
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ژورنال
عنوان ژورنال: Calcolo
سال: 2015
ISSN: 0008-0624,1126-5434
DOI: 10.1007/s10092-015-0159-7