Inverse Scattering on the Half-Line for ZS-AKNS Systems with Integrable Potentials
نویسندگان
چکیده
منابع مشابه
Inverse Resonance Scattering on the Half Line
For the Schrr odinger operator on the half line we prove the following results: the mapping from real compactly supported potentials to the associated Jost functions (in some class of entire functions) is one-to-one and onto. Moreover, we prove that such potential is uniquely determined by its bound states and resonances.
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is not assumed. Actually, if (3') holds, much more is known. In fact, in this case, there exist asymptotic formulas for the solutions of (1) whenX>0 ([8, p. 421]; cf. also [7, p. 258], in case/(<)—>0 as 2->oo) which guarantee, in particular, that 0^X<oo is in the continuous spectrum for every boundary value problem determined by (1) and (2). Obviously, the requirement (3) is compatible with T~i...
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Recently A. G. Ramm (1999) has shown that a subset of phase shifts δl, l = 0, 1, . . ., determines the potential if the indices of the known shifts satisfy the Müntz condition ∑ l =0,l∈L 1 l = ∞. We prove the necessity of this condition in some classes of potentials. The problem is reduced to an inverse eigenvalue problem for the half-line Schrödinger operators.
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Inverse problems for selfadjoint Schrödinger operators on the half line with compactly supported potentials Tuncay Aktosun,1,a) Paul Sacks,2,b) and Mehmet Unlu3,c) 1Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019-0408, USA 2Department of Mathematics, Iowa State University, Ames, Iowa 24061, USA 3Department of Mathematics, Recep Tayyip Erdogan University, 5310...
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The Schrödinger equation is considered on the line when the potential is real valued, compactly supported, and square integrable. The nonuniqueness is analyzed in the recovery of such a potential from the data consisting of the ratio of a corresponding reflection coefficient to the transmission coefficient. It is shown that there are a discrete number of potentials corresponding to the data and...
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ژورنال
عنوان ژورنال: Integral Equations and Operator Theory
سال: 2015
ISSN: 0378-620X,1420-8989
DOI: 10.1007/s00020-015-2269-7