{"id":"https://openalex.org/W7225001135","doi":"https://doi.org/10.1142/s0217984926502714","title":"Unveiling Solitary Waves and Chaotic Dynamics in the Non-Standard Nonlinear Schr\\\"{o}dinger Equation via Advanced Analytical Techniques","display_name":"Unveiling Solitary Waves and Chaotic Dynamics in the Non-Standard Nonlinear Schr\\\"{o}dinger Equation via Advanced Analytical Techniques","publication_year":2026,"publication_date":"2026-10-31","ids":{"openalex":"https://openalex.org/W7225001135","doi":"https://doi.org/10.1142/s0217984926502714"},"language":"en","primary_location":{"id":"doi:10.1142/s0217984926502714","doi":"https://doi.org/10.1142/s0217984926502714","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217984926502714","pdf_url":null,"source":{"id":"https://openalex.org/S88537382","display_name":"Modern Physics Letters B","issn_l":"0217-9849","issn":["0217-9849","1793-6640"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Modern Physics Letters B","raw_type":"journal-article"},"volume":null,"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/A5039120371","display_name":"Fatma Nur Kaya Sa\u011flam","orcid":"https://orcid.org/0000-0001-7488-3254","observed_orcids":["https://orcid.org/0000-0001-7488-3254"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fatma Nur Kaya Saglam","raw_affiliation_strings":[""],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055803510","display_name":"Sheikh Zain Majid","orcid":"https://orcid.org/0000-0003-3203-0207","observed_orcids":["https://orcid.org/0000-0003-3203-0207"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sheikh Zain Majid","raw_affiliation_strings":["https://orcid.org/0000-0003-3203-0207"],"raw_orcid":"https://orcid.org/0000-0003-3203-0207","affiliations":[{"raw_affiliation_string":"https://orcid.org/0000-0003-3203-0207","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.8349305,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9990000128746033,"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":0.9990000128746033,"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":0.00019999999494757503,"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"}},{"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"}}],"keywords":[{"id":"https://openalex.org/keywords/solitary-waves","display_name":"solitary waves","score":0.9629999995231628},{"id":"https://openalex.org/keywords/chaotic-dynamics","display_name":"chaotic dynamics","score":0.9120000004768372},{"id":"https://openalex.org/keywords/exact-traveling-wave-solutions","display_name":"exact traveling wave solutions","score":0.972000002861023},{"id":"https://openalex.org/keywords/g-g-expansion-method","display_name":"(G'/G)-expansion method","score":0.8040000200271606},{"id":"https://openalex.org/keywords/planar-dynamical-systems","display_name":"planar dynamical systems","score":0.8960000276565552},{"id":"https://openalex.org/keywords/phase-plane-analysis","display_name":"phase plane analysis","score":0.8579999804496765},{"id":"https://openalex.org/keywords/poincare-sections","display_name":"Poincar\u00e9 sections","score":0.8679999709129333},{"id":"https://openalex.org/keywords/bifurcation-analysis","display_name":"bifurcation analysis","score":0.9449999928474426},{"id":"https://openalex.org/keywords/quasi-periodic-regime","display_name":"quasi-periodic regime","score":0.628000020980835},{"id":"https://openalex.org/keywords/wave-propagation","display_name":"wave propagation","score":0.8100000023841858}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.7986999750137329},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.725600004196167},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6535000205039978},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6478000283241272},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5788000226020813},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5475000143051147},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5074999928474426},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.44589999318122864},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.44190001487731934},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4410000145435333},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.4316999912261963},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.42010000348091125},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.41029998660087585},{"id":"https://openalex.org/C21955772","wikidata":"https://www.wikidata.org/wiki/Q339199","display_name":"Poincar\u00e9 map","level":4,"score":0.3483999967575073},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.3427000045776367},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.3409000039100647},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.32839998602867126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31529998779296875},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C88221313","wikidata":"https://www.wikidata.org/wiki/Q203586","display_name":"Poincar\u00e9 conjecture","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.25450000166893005}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0217984926502714","doi":"https://doi.org/10.1142/s0217984926502714","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217984926502714","pdf_url":null,"source":{"id":"https://openalex.org/S88537382","display_name":"Modern Physics Letters B","issn_l":"0217-9849","issn":["0217-9849","1793-6640"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Modern Physics Letters B","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7169393342","https://openalex.org/W4391026925","https://openalex.org/W7167366826","https://openalex.org/W7213894088","https://openalex.org/W2023150856","https://openalex.org/W4401212434","https://openalex.org/W4411151531","https://openalex.org/W2392779841","https://openalex.org/W2053087572","https://openalex.org/W4220994758"],"abstract_inverted_index":{"In":[0],"this":[1,166],"paper,":[2],"we":[3],"study":[4],"the":[5,27,33,51,61,91,95,111,120,130,133,136,142,156,160,174],"dynamical":[6,48,67,148],"behaviour":[7,74],"and":[8,23,32,71,85,104,116,140,146,183],"exact":[9,42],"travelling":[10],"wave":[11,177],"solutions":[12,43],"of":[13,41,94,132,138,144,159,165,176,186],"a":[14,38,47,106],"non-standard":[15],"nonlinear":[16],"Schr\u00f6dinger":[17],"equation.":[18],"By":[19],"using":[20,77],"two":[21],"powerful":[22],"complementary":[24],"analytical":[25],"techniques,":[26],"[Formula:":[28,98],"see":[29,99],"text]-expansion":[30],"method":[31],"Newly":[34],"Improved":[35],"Kudryashov":[36],"method,":[37],"wide":[39],"family":[40],"are":[44,123,152],"constructed.":[45],"From":[46],"systems":[49],"perspective":[50],"equation":[52],"is":[53,69,75],"further":[54,172],"examined":[55],"to":[56,109,135,154],"get":[57],"deeper":[58],"insight":[59],"into":[60],"underlying":[62],"physical":[63,157],"mechanisms.":[64],"A":[65],"planar":[66],"system":[68,121,134],"derived":[70],"its":[72],"qualitative":[73],"analyzed":[76],"phase":[78],"portrait":[79],"analysis,":[80,82],"time-series":[81],"Poincare":[83],"section":[84],"three-dimensional":[86],"phase-space":[87],"trajectories.":[88],"We":[89],"investigate":[90],"bifurcation":[92,107,127],"structure":[93],"state":[96],"variable":[97],"text]":[100],"under":[101],"small":[102],"perturbations":[103],"perform":[105],"analysis":[108],"demonstrate":[110],"transition":[112],"between":[113],"periodic,":[114],"quasi-periodic":[115],"chaotic":[117],"regimes":[118],"as":[119],"parameters":[122,139],"varied.":[124],"The":[125,163],"obtained":[126,161],"diagrams":[128],"confirm":[129],"sensitivity":[131],"variation":[137],"exhibit":[141],"coexistence":[143],"stable":[145],"unstable":[147],"structures.":[149],"Graphical":[150],"simulations":[151],"provided":[153],"visualize":[155],"meaning":[158],"solutions.":[162],"results":[164],"work":[167],"can":[168],"be":[169],"useful":[170],"for":[171],"understanding":[173],"phenomena":[175],"propagation":[178],"in":[179],"oceans,":[180],"plasma":[181],"physics,":[182],"other":[184],"areas":[185],"mathematical":[187],"physics.":[188]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-11-01T00:00:00"}
