{"id":"https://openalex.org/W2531391688","doi":"https://doi.org/10.1137/16m1055700","title":"The Linear Stability of a Wavetrain Propagating on Water of Variable Depth","display_name":"The Linear Stability of a Wavetrain Propagating on Water of Variable Depth","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2531391688","doi":"https://doi.org/10.1137/16m1055700","mag":"2531391688"},"language":"en","primary_location":{"id":"doi:10.1137/16m1055700","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1055700","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/A5074229824","display_name":"Girish Kumar Rajan","orcid":"https://orcid.org/0000-0002-1844-0974"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Girish K. Rajan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056181686","display_name":"D. M. Henderson","orcid":"https://orcid.org/0000-0001-8646-0005"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diane M. Henderson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074229824"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.06890093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"76","issue":"5","first_page":"2030","last_page":"2041"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11061","display_name":"Ocean Waves and Remote Sensing","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11061","display_name":"Ocean Waves and Remote Sensing","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10647","display_name":"Coastal and Marine Dynamics","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1904","display_name":"Earth-Surface Processes"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.8376359343528748},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.7654898166656494},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.7184581756591797},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5811466574668884},{"id":"https://openalex.org/keywords/modulational-instability","display_name":"Modulational instability","score":0.5735848546028137},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.5584756135940552},{"id":"https://openalex.org/keywords/envelope","display_name":"Envelope (radar)","score":0.5448881983757019},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5310153365135193},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5219458937644958},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.5059482455253601},{"id":"https://openalex.org/keywords/bathymetry","display_name":"Bathymetry","score":0.49634867906570435},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4640817642211914},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.18849226832389832},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.10186100006103516},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.07669621706008911}],"concepts":[{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.8376359343528748},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.7654898166656494},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.7184581756591797},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5811466574668884},{"id":"https://openalex.org/C125755039","wikidata":"https://www.wikidata.org/wiki/Q17104082","display_name":"Modulational instability","level":3,"score":0.5735848546028137},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.5584756135940552},{"id":"https://openalex.org/C65155139","wikidata":"https://www.wikidata.org/wiki/Q5380912","display_name":"Envelope (radar)","level":3,"score":0.5448881983757019},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5310153365135193},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5219458937644958},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5059482455253601},{"id":"https://openalex.org/C174943157","wikidata":"https://www.wikidata.org/wiki/Q810826","display_name":"Bathymetry","level":2,"score":0.49634867906570435},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4640817642211914},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.18849226832389832},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.10186100006103516},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.07669621706008911},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"score":0.0},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1055700","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1055700","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6","score":0.4300000071525574}],"awards":[{"id":"https://openalex.org/G3935486414","display_name":null,"funder_award_id":"1107379","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W90144665","https://openalex.org/W149201185","https://openalex.org/W1510048705","https://openalex.org/W1558118357","https://openalex.org/W1571313600","https://openalex.org/W1969428562","https://openalex.org/W1971647916","https://openalex.org/W1986788497","https://openalex.org/W2004657108","https://openalex.org/W2006551339","https://openalex.org/W2033673401","https://openalex.org/W2038445490","https://openalex.org/W2047424724","https://openalex.org/W2049789781","https://openalex.org/W2049915610","https://openalex.org/W2051842180","https://openalex.org/W2059509946","https://openalex.org/W2079363621","https://openalex.org/W2090181333","https://openalex.org/W2090885565","https://openalex.org/W2096254855","https://openalex.org/W2099317565","https://openalex.org/W2100886722","https://openalex.org/W2103394053","https://openalex.org/W2106761962","https://openalex.org/W2114130739","https://openalex.org/W2121614103","https://openalex.org/W2127965024","https://openalex.org/W2131843779","https://openalex.org/W2136593750","https://openalex.org/W2140667609","https://openalex.org/W2141237926","https://openalex.org/W2160666906","https://openalex.org/W2169302697","https://openalex.org/W2318018936","https://openalex.org/W2329231534","https://openalex.org/W2994685737","https://openalex.org/W3097859411","https://openalex.org/W3152192480","https://openalex.org/W4210506996"],"related_works":["https://openalex.org/W2073827472","https://openalex.org/W2033338910","https://openalex.org/W2793357704","https://openalex.org/W4386617716","https://openalex.org/W2184765375","https://openalex.org/W3152163876","https://openalex.org/W773765100","https://openalex.org/W2102699260","https://openalex.org/W2622615123","https://openalex.org/W1997728991"],"abstract_inverted_index":{"A":[0],"narrow-banded":[1],"spectrum":[2],"of":[3,14,49,94],"gravity":[4],"waves":[5,139,156],"propagating":[6,140,157],"in":[7,36,71,90,125],"one":[8],"horizontal":[9],"direction":[10],"at":[11],"the":[12,29,34,37,64,83,100,106,126,152],"surface":[13],"water":[15],"with":[16,105],"finite":[17],"depth":[18,30],"may":[19,56,75],"be":[20],"governed":[21],"by":[22],"a":[23,59,78,113,119],"nonlinear":[24],"Schr\u00f6dinger":[25],"equation":[26],"(NLSE).":[27],"If":[28],"is":[31,53],"nonuniform,":[32],"then":[33],"coefficients":[35],"NLSE":[38],"are":[39],"variable":[40],"and":[41,69,88,130,146],"an":[42],"additional":[43],"linear":[44,133],"term":[45,61,80],"due":[46],"to":[47,67,86,150,163],"conservation":[48],"wave":[50,65,84],"action":[51],"flux":[52],"present,":[54],"which":[55,74],"act":[57,76,149],"as":[58,77],"dissipative":[60,101,115],"that":[62,81,121,137],"causes":[63,82,170],"envelope":[66,85],"broaden":[68],"decrease":[70],"amplitude":[72,124],"or":[73,103],"growth":[79,107],"focus":[87],"increase":[89],"amplitude.":[91],"The":[92],"addition":[93],"linear,":[95],"viscous":[96,147,167],"dissipation":[97,148,168],"either":[98],"enhances":[99],"process":[102],"competes":[104],"effect.":[108],"Here":[109],"we":[110],"consider":[111],"such":[112],"variable-coefficient,":[114],"NLSE.":[116],"We":[117,135],"find":[118,136],"solution":[120],"has":[122],"uniform":[123],"appropriate":[127],"reference":[128],"frame":[129],"examine":[131],"its":[132],"stability.":[134],"for":[138,172],"into":[141,158],"shallower":[142],"water,":[143,160],"both":[144],"bathymetry":[145,161],"stabilize":[151],"modulational":[153],"instability.":[154],"For":[155],"deeper":[159],"acts":[162],"enhance":[164],"instability,":[165],"but":[166],"eventually":[169],"stabilization":[171],"small":[173],"enough":[174],"initial":[175],"perturbation":[176],"amplitudes.":[177]},"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":8},{"year":2022,"cited_by_count":1}],"updated_date":"2026-02-28T09:26:25.869077","created_date":"2025-10-10T00:00:00"}
