{"id":"https://openalex.org/W2056369396","doi":"https://doi.org/10.1007/s00332-010-9077-7","title":"Justification of the Ginzburg\u2013Landau Approximation in Case of Marginally Stable Long Waves","display_name":"Justification of the Ginzburg\u2013Landau Approximation in Case of Marginally Stable Long Waves","publication_year":2010,"publication_date":"2010-10-07","ids":{"openalex":"https://openalex.org/W2056369396","doi":"https://doi.org/10.1007/s00332-010-9077-7","mag":"2056369396"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-010-9077-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-010-9077-7","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","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/A5047484404","display_name":"Tobias H\u00e4cker","orcid":"https://orcid.org/0000-0001-5057-6313"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias H\u00e4cker","raw_affiliation_strings":["Institut f\u00fcr Analysis, Dynamik und Modellierung, Universit\u00e4t Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany","Universit\u00e4t Stuttgart"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis, Dynamik und Modellierung, Universit\u00e4t Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]},{"raw_affiliation_string":"Universit\u00e4t Stuttgart","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053506285","display_name":"Guido Schneider","orcid":"https://orcid.org/0000-0002-9689-6299"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Guido Schneider","raw_affiliation_strings":["Institut f\u00fcr Analysis, Dynamik und Modellierung, Universit\u00e4t Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany","Universit\u00e4t Stuttgart"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis, Dynamik und Modellierung, Universit\u00e4t Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]},{"raw_affiliation_string":"Universit\u00e4t Stuttgart","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110290405","display_name":"Dominik Zimmermann","orcid":null},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dominik Zimmermann","raw_affiliation_strings":["Institut f\u00fcr Analysis, Dynamik und Modellierung, Universit\u00e4t Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany","Universit\u00e4t Stuttgart"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis, Dynamik und Modellierung, Universit\u00e4t Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]},{"raw_affiliation_string":"Universit\u00e4t Stuttgart","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053506285"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.8104,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.8007409,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"1","first_page":"93","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9739000201225281,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6222826838493347},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6172797083854675},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.6039003729820251},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5843348503112793},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5614956617355347},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5298570990562439},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.52442467212677},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.48001188039779663},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4345892369747162},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4276847541332245},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42611706256866455},{"id":"https://openalex.org/keywords/wavenumber","display_name":"Wavenumber","score":0.42490246891975403},{"id":"https://openalex.org/keywords/inclined-plane","display_name":"Inclined plane","score":0.42330318689346313},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3796330690383911},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3528258800506592},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16127175092697144},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13376227021217346}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6222826838493347},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6172797083854675},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.6039003729820251},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5843348503112793},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5614956617355347},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5298570990562439},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.52442467212677},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.48001188039779663},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4345892369747162},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4276847541332245},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42611706256866455},{"id":"https://openalex.org/C121130766","wikidata":"https://www.wikidata.org/wiki/Q192510","display_name":"Wavenumber","level":2,"score":0.42490246891975403},{"id":"https://openalex.org/C111808769","wikidata":"https://www.wikidata.org/wiki/Q161462","display_name":"Inclined plane","level":2,"score":0.42330318689346313},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3796330690383911},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3528258800506592},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16127175092697144},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13376227021217346},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00332-010-9077-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-010-9077-7","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5600000023841858}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1964296541","https://openalex.org/W1977771619","https://openalex.org/W2019806348","https://openalex.org/W2020222074","https://openalex.org/W2020424090","https://openalex.org/W2020772938","https://openalex.org/W2023730753","https://openalex.org/W2028974253","https://openalex.org/W2035303651","https://openalex.org/W2047926208","https://openalex.org/W2057622389","https://openalex.org/W2072059296","https://openalex.org/W2072465500","https://openalex.org/W2073920200","https://openalex.org/W2078457525","https://openalex.org/W2081179525","https://openalex.org/W2089259611","https://openalex.org/W2098631697","https://openalex.org/W2105103650","https://openalex.org/W2111059884","https://openalex.org/W2117915059","https://openalex.org/W2141348593","https://openalex.org/W2145965567","https://openalex.org/W2149453355","https://openalex.org/W2157495020","https://openalex.org/W2170019858","https://openalex.org/W2269737763","https://openalex.org/W2316448142"],"related_works":["https://openalex.org/W3148450583","https://openalex.org/W2001088508","https://openalex.org/W1977973012","https://openalex.org/W4238008884","https://openalex.org/W1506249783","https://openalex.org/W4376130101","https://openalex.org/W2332152992","https://openalex.org/W1970871817","https://openalex.org/W4300407647","https://openalex.org/W2099381872"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
