{"id":"https://openalex.org/W2054859577","doi":"https://doi.org/10.4236/am.2012.310168","title":"The Basic (G'/G)-Expansion Method for the Fourth Order Boussinesq Equation","display_name":"The Basic (G'/G)-Expansion Method for the Fourth Order Boussinesq Equation","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2054859577","doi":"https://doi.org/10.4236/am.2012.310168","mag":"2054859577"},"language":"en","primary_location":{"id":"doi:10.4236/am.2012.310168","doi":"https://doi.org/10.4236/am.2012.310168","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2012.310168","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=23371","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=23371","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009759160","display_name":"Hasibun Naher","orcid":"https://orcid.org/0000-0002-7669-2037","observed_orcids":["https://orcid.org/0000-0002-7669-2037"]},"institutions":[{"id":"https://openalex.org/I139322472","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63","country_code":"MY","type":"education","lineage":["https://openalex.org/I139322472"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Hasibun Naher","raw_affiliation_strings":["School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia","institution_ids":["https://openalex.org/I139322472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019785333","display_name":"Farah Aini Abdullah","orcid":"https://orcid.org/0000-0002-5215-9617","observed_orcids":["https://orcid.org/0000-0002-5215-9617"]},"institutions":[{"id":"https://openalex.org/I139322472","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63","country_code":"MY","type":"education","lineage":["https://openalex.org/I139322472"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Farah Aini Abdullah","raw_affiliation_strings":["School of Mathematical Sciences , Universiti Sains Malaysia , Penang , Malaysia","Universiti Sains, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Universiti Sains Malaysia , Penang , Malaysia","institution_ids":["https://openalex.org/I139322472"]},{"raw_affiliation_string":"Universiti Sains, Malaysia","institution_ids":["https://openalex.org/I139322472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I139322472"],"apc_list":null,"apc_paid":null,"fwci":3.2211,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.92702274,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"03","issue":"10","first_page":"1144","last_page":"1152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994999766349792,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994999766349792,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0,"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/g-g-expansion-method","display_name":"(G'/G)-expansion method","score":0.9620000123977661},{"id":"https://openalex.org/keywords/traveling-wave-solutions","display_name":"traveling wave solutions","score":0.9279999732971191},{"id":"https://openalex.org/keywords/exact-solutions","display_name":"exact solutions","score":0.9049999713897705},{"id":"https://openalex.org/keywords/solitons","display_name":"solitons","score":0.8650000095367432},{"id":"https://openalex.org/keywords/periodic-solutions","display_name":"periodic solutions","score":0.9990000128746033},{"id":"https://openalex.org/keywords/nonlinear-partial-differential-equations","display_name":"nonlinear partial differential equations","score":0.8330000042915344},{"id":"https://openalex.org/keywords/second-order-linear-ordinary-differential-equations","display_name":"second-order linear ordinary differential equations","score":0.7009999752044678}],"concepts":[{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.7289280891418457},{"id":"https://openalex.org/C2780414537","wikidata":"https://www.wikidata.org/wiki/Q42292","display_name":"Maple","level":2,"score":0.6734739542007446},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5732232928276062},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5718053579330444},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5677856206893921},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5446287393569946},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5294660329818726},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4715963304042816},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.44971713423728943},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43341606855392456},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42397499084472656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29053640365600586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1280023455619812},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07371288537979126},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4236/am.2012.310168","doi":"https://doi.org/10.4236/am.2012.310168","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2012.310168","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=23371","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.852.2833","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.852.2833","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.scirp.org/journal/PaperDownload.aspx?paperID%3D23371","raw_type":"text"}],"best_oa_location":{"id":"doi:10.4236/am.2012.310168","doi":"https://doi.org/10.4236/am.2012.310168","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2012.310168","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=23371","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054859577.pdf","grobid_xml":"https://content.openalex.org/works/W2054859577.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1966459141","https://openalex.org/W1968818156","https://openalex.org/W1970856135","https://openalex.org/W1978690683","https://openalex.org/W1979319996","https://openalex.org/W1983238108","https://openalex.org/W1985948414","https://openalex.org/W1989760690","https://openalex.org/W1990902908","https://openalex.org/W2001466999","https://openalex.org/W2003767680","https://openalex.org/W2005509873","https://openalex.org/W2009999606","https://openalex.org/W2010246090","https://openalex.org/W2013257838","https://openalex.org/W2015613929","https://openalex.org/W2019176245","https://openalex.org/W2027147139","https://openalex.org/W2027588087","https://openalex.org/W2031454797","https://openalex.org/W2033734904","https://openalex.org/W2034451744","https://openalex.org/W2038152558","https://openalex.org/W2048920804","https://openalex.org/W2051104414","https://openalex.org/W2052110998","https://openalex.org/W2053833421","https://openalex.org/W2057298042","https://openalex.org/W2061496940","https://openalex.org/W2062575419","https://openalex.org/W2062682248","https://openalex.org/W2065211610","https://openalex.org/W2069428234","https://openalex.org/W2071863692","https://openalex.org/W2072009618","https://openalex.org/W2073817609","https://openalex.org/W2082638549","https://openalex.org/W2083332431","https://openalex.org/W2083960709","https://openalex.org/W2084880168","https://openalex.org/W2086698446","https://openalex.org/W2087222117","https://openalex.org/W2090673375","https://openalex.org/W2094000073","https://openalex.org/W2094892214","https://openalex.org/W2095431296","https://openalex.org/W2132720389","https://openalex.org/W2141112962","https://openalex.org/W2202622074","https://openalex.org/W2289888184","https://openalex.org/W2385653024","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W7135159575","https://openalex.org/W1551159732","https://openalex.org/W2116445026","https://openalex.org/W1990442246","https://openalex.org/W1987649080","https://openalex.org/W2955499290","https://openalex.org/W2122780141","https://openalex.org/W2372616955","https://openalex.org/W1991832864","https://openalex.org/W2590267943"],"abstract_inverted_index":{"The":[0],"(G'/G)-expansion":[1,56],"method":[2],"is":[3,75],"simple":[4],"and":[5,25,80],"powerful":[6],"mathematical":[7,23],"tool":[8],"for":[9],"constructing":[10],"traveling":[11,37],"wave":[12,38],"solutions":[13,39,82,94],"of":[14,40,64,92,103],"nonlinear":[15,42],"evolution":[16],"equations":[17],"which":[18],"arise":[19],"in":[20,97],"engineering":[21],"sciences,":[22],"physics":[24],"real":[26],"time":[27],"application":[28],"fields.":[29],"In":[30,58,89],"this":[31,59],"article,":[32],"we":[33],"have":[34],"obtained":[35,93],"exact":[36],"the":[41,47,55,61,65,78,98,101],"partial":[43],"differential":[44,70],"equation,":[45],"namely,":[46],"fourth":[48],"order":[49,67],"Boussinesq":[50],"equation":[51,71],"involving":[52],"parameters":[53],"via":[54],"method.":[57],"method,":[60],"general":[62],"solution":[63],"second":[66],"linear":[68],"ordinary":[69],"with":[72,100],"constant":[73],"coefficients":[74],"implemented.":[76],"Further,":[77],"solitons":[79],"periodic":[81],"are":[83,95],"described":[84,96],"through":[85],"three":[86],"different":[87],"families.":[88],"addition,":[90],"some":[91],"figures":[99],"aid":[102],"commercial":[104],"software":[105],"Maple.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":4}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}