{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T09:23:40Z","timestamp":1768296220545,"version":"3.49.0"},"reference-count":80,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"12","license":[{"start":{"date-parts":[[2015,12,1]],"date-time":"2015-12-01T00:00:00Z","timestamp":1448928000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"funder":[{"name":"German Research Foundation (DFG)","award":["WA 3139\/1-1"],"award-info":[{"award-number":["WA 3139\/1-1"]}]},{"DOI":"10.13039\/100000001","name":"U. S. National Science Foundation","doi-asserted-by":"crossref","award":["CCF-1420575"],"award-info":[{"award-number":["CCF-1420575"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2015,12]]},"DOI":"10.1109\/tit.2015.2485944","type":"journal-article","created":{"date-parts":[[2015,10,1]],"date-time":"2015-10-01T15:06:39Z","timestamp":1443711999000},"page":"6957-6974","source":"Crossref","is-referenced-by-count":115,"title":["Fast Numerical Nonlinear Fourier Transforms"],"prefix":"10.1109","volume":"61","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5159-0918","authenticated-orcid":false,"given":"Sander","family":"Wahls","sequence":"first","affiliation":[]},{"given":"H. Vincent","family":"Poor","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/45\/25\/255205"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1979.1084580"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.2307\/2001916"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1145\/1555386.1555388"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1007\/BF02745257"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(79)90833-8"},{"key":"ref74","first-page":"248","article-title":"On the theory of two-dimensional stationary self-focusing of electromagnetic waves","volume":"38","author":"manakov","year":"1974","journal-title":"J Experim Theoretical Phys"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1364\/OL.38.004186"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.54.396"},{"key":"ref38","first-page":"1848","article-title":"Inverse nonlinear Fourier transforms via interpolation: The Ablowitz–Ladik Case","author":"wahls","year":"2014","journal-title":"Proc 21st Int Symp Math Theory Netw Syst (MTNS)"},{"key":"ref78","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.51.3036"},{"key":"ref79","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.74.239"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-03-01609-0"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160481203"},{"key":"ref31","article-title":"The inverse spectral solution, modulation theory and linearized stability analysis of n-phase, quasi-periodic solutions of the nonlinear Schrödinger equation","author":"lee","year":"1986"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/BF01018207"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/QBSC.2014.6841191"},{"key":"ref36","article-title":"Studies of the cubic Schrödinger equation","author":"ma","year":"1977"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1981652113"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1140\/epjst\/e2010-01251-x"},{"key":"ref60","article-title":"A CMV–based eigensolver for companion matrices","author":"bevilacqua","year":"2014"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6087"},{"key":"ref61","article-title":"Techniques and instabilities for 1 + 1 and 2 + 1 dimensional integrable partial differential equations","author":"macevoy","year":"1994"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1109\/20.767268"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.37.815"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.03.020"},{"key":"ref27","article-title":"Topics in nonlinear wave theory with applications","author":"tracy","year":"1984"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(92)90370-E"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.2307\/2589209"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8689-6_3"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385702000482"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1007\/s002220100149"},{"key":"ref69","article-title":"On the speed of convergence of Newton’s method for complex polynomials","author":"bilarev","year":"2012"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1049\/el:19950701"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-46064-0"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1115\/OMAE2012-83418"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2007.2055"},{"key":"ref21","article-title":"Data analysis techniques for resolving nonlinear processes in plasmas: A review","author":"dudok de wit","year":"1996"},{"key":"ref24","first-page":"121","article-title":"Periodic problem for the nonlinear Schrödinger equation","volume":"1","author":"kotlyarov","year":"1976","journal-title":"Problems Math Phys Funct Anal (Naukova Dumka Kiev)"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(01)00155-5"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.53.218"},{"key":"ref25","first-page":"965","article-title":"Explicit formulas for solutions of the nonlinear Schrödinger equation","volume":"11","author":"its","year":"1976","journal-title":"Dokl Akad Nauk UkrSSR Ser A"},{"key":"ref50","article-title":"The relationship between the spectral theories for the periodic Korteweg–deVries and nonlinear Schrödinger equations","author":"tracy","year":"1991","journal-title":"Nonlinear Topics In Ocean Physics"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1038\/nature06402"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1016\/j.indag.2012.05.006"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-010-0302-y"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7643-8539-2_7"},{"key":"ref56","author":"kamen","year":"2007","journal-title":"Fundamentals of Signals and Systems using the Web and Matlab"},{"key":"ref55","author":"burrus","year":"2012","journal-title":"Horner’s Method for Evaluating and Deflating Polynomials"},{"key":"ref54","volume":"302","author":"ablowitz","year":"2004","journal-title":"Discrete and Continuous Nonlinear Schrödinger Systems"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(96)00057-2"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1063\/1.523009"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2321155"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/JLT.2009.2039464"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.013901"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/JPHOT.2012.2189379"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/50.219570"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1364\/OE.21.024344"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2013.6638772"},{"key":"ref16","article-title":"Information transmission using the nonlinear Fourier transform","author":"yousefi","year":"2013"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(93)90319-U"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2009.06.005"},{"key":"ref19","author":"osborne","year":"2010","journal-title":"Nonlinear Ocean Waves and the Inverse Scattering Transform"},{"key":"ref80","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/34\/33\/101"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/5\/2\/009"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(97)00073-2"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.19.1095"},{"key":"ref5","first-page":"62","article-title":"Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of wave in nonlinear media","volume":"34","author":"zakharov","year":"1972","journal-title":"J Experim Theoretical Phys"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2321151"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1974534249"},{"key":"ref49","volume":"144","author":"teschl","year":"2010","journal-title":"Ordinary Differential Equations and Dynamical Systems"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2321151"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1007\/BF02789306"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1007\/BF02105191"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160210503"},{"key":"ref47","volume":"50","author":"eckhaus","year":"1981","journal-title":"The Inverse Scattering Transformation and the Theory of Solitons An Introduction"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2014.6875345"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1364\/OE.22.026720"},{"key":"ref44","article-title":"Numerical and analytical studies of the discrete nonlinear Schröedinger equation","author":"schober","year":"1991"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(86)90086-2"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/7331248\/07286836.pdf?arnumber=7286836","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T11:45:26Z","timestamp":1641987926000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/7286836\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12]]},"references-count":80,"journal-issue":{"issue":"12"},"URL":"https:\/\/doi.org\/10.1109\/tit.2015.2485944","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12]]}}}