Inverse scattering in one-dimensional nonconservative media |
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| Authors: | Tuncay Aktosun Martin Klaus Cornelis van der Mee |
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| Institution: | (1) Dept. of Mathematics, North Dakota State Univ., 58105 Fargo, ND;(2) Dept. of Mathematics, Virginia Polytechnic Inst. and State Univ., 24061 Blacksburg, VA;(3) Dipartimento di Matematica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy |
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| Abstract: | The inverse scattering problem arising in wave propagation in one-dimensional non-conservative media is analyzed. This is done in the frequency domain by considering the Schrödinger equation with the potentialikP(x)+Q(x), wherek
2 is the energy andP(x) andQ(x) are real integrable functions. Using a pair of uncoupled Marchenko integral equations,P(x) andQ(x) are recovered from an appropriate set of scattering data including bound-state information. Some illustrative examples are provided.Dedicated to M.G. Kreîn, one of the founding fathers of inverse scattering theory. |
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| Keywords: | 34A55 81U40 Secondary 73D50 |
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