{"id":"https://openalex.org/W1988197195","doi":"https://doi.org/10.1137/s0036139902400477","title":"Averaging of Dispersion-Managed Solitons: Existence and Stability","display_name":"Averaging of Dispersion-Managed Solitons: Existence and Stability","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1988197195","doi":"https://doi.org/10.1137/s0036139902400477","mag":"1988197195"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139902400477","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902400477","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046714116","display_name":"Dmitry E. Pelinovsky","orcid":"https://orcid.org/0000-0001-5812-440X"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Dmitry E. Pelinovsky","raw_affiliation_strings":["McMaster university#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"McMaster university#TAB#","institution_ids":["https://openalex.org/I98251732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005202787","display_name":"Vadim Zharnitsky","orcid":"https://orcid.org/0000-0003-3417-8993"},"institutions":[{"id":"https://openalex.org/I1322087612","display_name":"Alcatel Lucent (Germany)","ror":"https://ror.org/00c5mwp75","country_code":"DE","type":"company","lineage":["https://openalex.org/I1322087612"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Vadim Zharnitsky","raw_affiliation_strings":["Lucent"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lucent","institution_ids":["https://openalex.org/I1322087612"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8173,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.90459511,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"63","issue":"3","first_page":"745","last_page":"776"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.7653940916061401},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6498045921325684},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5699756145477295},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5616829991340637},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5103992819786072},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.48862916231155396},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.4838065505027771},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.4752759039402008},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4420081675052643},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4200391471385956},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3971109092235565},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.391704261302948},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.2660543620586395},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.23043066263198853}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.7653940916061401},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6498045921325684},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5699756145477295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5616829991340637},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5103992819786072},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.48862916231155396},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.4838065505027771},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.4752759039402008},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4420081675052643},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4200391471385956},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3971109092235565},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.391704261302948},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.2660543620586395},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.23043066263198853},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139902400477","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902400477","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.138.7180","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.7180","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/~vz/vz_peli.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W92681173","https://openalex.org/W1496798092","https://openalex.org/W1628909031","https://openalex.org/W1966163759","https://openalex.org/W1966329783","https://openalex.org/W1988088155","https://openalex.org/W2001765743","https://openalex.org/W2016720595","https://openalex.org/W2042754733","https://openalex.org/W2042820187","https://openalex.org/W2043334970","https://openalex.org/W2050506799","https://openalex.org/W2051089144","https://openalex.org/W2058006423","https://openalex.org/W2061258373","https://openalex.org/W2067823795","https://openalex.org/W2071844352","https://openalex.org/W2078262972","https://openalex.org/W2095977033","https://openalex.org/W2096004969","https://openalex.org/W2098485838","https://openalex.org/W2112201696","https://openalex.org/W2118523190","https://openalex.org/W2124193434","https://openalex.org/W2135909171","https://openalex.org/W2166983143","https://openalex.org/W2461228432","https://openalex.org/W4244924712","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2075972694","https://openalex.org/W1974817520","https://openalex.org/W2153532271","https://openalex.org/W2953057646","https://openalex.org/W2350430547","https://openalex.org/W2529347948","https://openalex.org/W2391633779","https://openalex.org/W2062124054","https://openalex.org/W2021832449","https://openalex.org/W3208349892"],"abstract_inverted_index":{"We":[0,34],"consider":[1],"existence":[2],"and":[3,27,41,65,87],"stability":[4],"of":[5,12,62,71,74,81,90],"dispersion-managed":[6,95],"solitons":[7,96],"in":[8,97],"the":[9,13,51,75,82,88,98],"two":[10],"approximations":[11],"periodic":[14,46],"nonlinear":[15],"Schr\u00f6dinger":[16],"(NLS)":[17],"equation:":[18],"(i)":[19],"a":[20,24],"dynamical":[21],"system":[22],"for":[23,39,58],"Gaussian":[25],"pulse":[26],"(ii)":[28],"an":[29],"average":[30],"integral":[31],"NLS":[32],"equation.":[33],"apply":[35],"normal":[36],"form":[37],"transformations":[38],"finite-dimensional":[40],"infinite-dimensional":[42],"Hamiltonian":[43,54,100],"systems":[44],"with":[45],"coefficients.":[47],"First-order":[48],"corrections":[49],"to":[50,94],"leading-order":[52],"averaged":[53,77,99],"are":[55],"derived":[56],"explicitly":[57],"both":[59],"approximations.":[60],"Bifurcations":[61],"soliton":[63],"solutions":[64],"their":[66],"stabilityare":[67],"studied":[68],"by":[69],"analysis":[70],"critical":[72],"points":[73],"first-order":[76],"Hamiltonians.":[78],"The":[79],"validity":[80],"averaging":[83],"procedure":[84],"is":[85,101],"verified":[86],"presence":[89],"ground":[91],"states":[92],"corresponding":[93],"established.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
