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Inverse scattering: solution of coupled Gel'fand-Levitan-Marchenko integral equations using successive kernel approximations
We develop a method of successive kernel approximations to solve coupled Gel'fand-Levitan-Marchenko (1955) integral equations. These equations appear in the synthesis problem of nonuniform and lossy transmission lines, the inversion of absorbing dielectrics and wavenumber-dependent potentials,...
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| Published in: | IEEE transactions on antennas and propagation 1995-06, Vol.43 (6), p.547-552 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c335t-18a32df06fbda477e6ce38e3af0a5507f9b35ee2bb74b6151e0c679b95568a933 |
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| cites | cdi_FETCH-LOGICAL-c335t-18a32df06fbda477e6ce38e3af0a5507f9b35ee2bb74b6151e0c679b95568a933 |
| container_end_page | 552 |
| container_issue | 6 |
| container_start_page | 547 |
| container_title | IEEE transactions on antennas and propagation |
| container_volume | 43 |
| creator | Frangos, F.V. Jaggard, D.L. |
| description | We develop a method of successive kernel approximations to solve coupled Gel'fand-Levitan-Marchenko (1955) integral equations. These equations appear in the synthesis problem of nonuniform and lossy transmission lines, the inversion of absorbing dielectrics and wavenumber-dependent potentials, the design of corrugated waveguide filters, soliton theory, and other applications. We find that our method is easy to apply, more accurate than previously developed methods, and can be used for a larger number of applications when compared to prior work. As an application and example, wavenumber-dependent potentials are reconstructed from scattering data.< > |
| doi_str_mv | 10.1109/8.387169 |
| format | article |
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These equations appear in the synthesis problem of nonuniform and lossy transmission lines, the inversion of absorbing dielectrics and wavenumber-dependent potentials, the design of corrugated waveguide filters, soliton theory, and other applications. We find that our method is easy to apply, more accurate than previously developed methods, and can be used for a larger number of applications when compared to prior work. 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As an application and example, wavenumber-dependent potentials are reconstructed from scattering data.< ></description><subject>Applied sciences</subject><subject>Couplings</subject><subject>Dielectric losses</subject><subject>Diffraction, scattering, reflection</subject><subject>Exact sciences and technology</subject><subject>Filtering theory</subject><subject>Filters</subject><subject>Integral equations</subject><subject>Inverse problems</subject><subject>Kernel</subject><subject>Propagation losses</subject><subject>Radiocommunications</subject><subject>Radiowave propagation</subject><subject>Telecommunications</subject><subject>Telecommunications and information theory</subject><subject>Transmission line theory</subject><subject>Waveguide theory</subject><issn>0018-926X</issn><issn>1558-2221</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><recordid>eNqFkc1LxDAQxYMouH6AZ085iHqpJk2Tpt5k8QtWvCh4K2l2otGYrpl2UfCPt0tFj56GYX7zHjOPkD3OTjhn1ak-EbrkqlojEy6lzvI85-tkwhjXWZWrx02yhfgytIUuign5uolLSAgUrek6SD4-nVFsQ9_5NtLWUdv2iwBzegXhyJk4z2aw9J2J2a1J9hnia0t97OApmUDhvTerPaQ9DkIUe2sB0S-BvkKKEKhZLFL74d9GbIdsOBMQdn_qNnm4vLifXmezu6ub6fkss0LILuPaiHzumHLN3BRlCcqC0CCMY0ZKVrqqERIgb5qyaBSXHJhVZdVUUiptKiG2yeGoO5i_94Bd_ebRQggmQttjnetCcaXz_0FZMVlINYDHI2hTi5jA1Ys0XJU-a87qVQ61rsccBvTgR9MMPw4umWg9_vJCllKKlfX-iHkA-JuOGt_XP5J6</recordid><startdate>19950601</startdate><enddate>19950601</enddate><creator>Frangos, F.V.</creator><creator>Jaggard, D.L.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7SP</scope></search><sort><creationdate>19950601</creationdate><title>Inverse scattering: solution of coupled Gel'fand-Levitan-Marchenko integral equations using successive kernel approximations</title><author>Frangos, F.V. ; Jaggard, D.L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c335t-18a32df06fbda477e6ce38e3af0a5507f9b35ee2bb74b6151e0c679b95568a933</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1995</creationdate><topic>Applied sciences</topic><topic>Couplings</topic><topic>Dielectric losses</topic><topic>Diffraction, scattering, reflection</topic><topic>Exact sciences and technology</topic><topic>Filtering theory</topic><topic>Filters</topic><topic>Integral equations</topic><topic>Inverse problems</topic><topic>Kernel</topic><topic>Propagation losses</topic><topic>Radiocommunications</topic><topic>Radiowave propagation</topic><topic>Telecommunications</topic><topic>Telecommunications and information theory</topic><topic>Transmission line theory</topic><topic>Waveguide theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Frangos, F.V.</creatorcontrib><creatorcontrib>Jaggard, D.L.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Electronics & Communications Abstracts</collection><jtitle>IEEE transactions on antennas and propagation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Frangos, F.V.</au><au>Jaggard, D.L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Inverse scattering: solution of coupled Gel'fand-Levitan-Marchenko integral equations using successive kernel approximations</atitle><jtitle>IEEE transactions on antennas and propagation</jtitle><stitle>TAP</stitle><date>1995-06-01</date><risdate>1995</risdate><volume>43</volume><issue>6</issue><spage>547</spage><epage>552</epage><pages>547-552</pages><issn>0018-926X</issn><eissn>1558-2221</eissn><coden>IETPAK</coden><abstract>We develop a method of successive kernel approximations to solve coupled Gel'fand-Levitan-Marchenko (1955) integral equations. 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| ispartof | IEEE transactions on antennas and propagation, 1995-06, Vol.43 (6), p.547-552 |
| issn | 0018-926X 1558-2221 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_3575532 |
| source | IEEE Electronic Library (IEL) Journals |
| subjects | Applied sciences Couplings Dielectric losses Diffraction, scattering, reflection Exact sciences and technology Filtering theory Filters Integral equations Inverse problems Kernel Propagation losses Radiocommunications Radiowave propagation Telecommunications Telecommunications and information theory Transmission line theory Waveguide theory |
| title | Inverse scattering: solution of coupled Gel'fand-Levitan-Marchenko integral equations using successive kernel approximations |
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