{"id":"https://openalex.org/W7115190868","doi":"https://doi.org/10.1142/s0218127426500392","title":"Periodic Traveling Wave Solutions of a Singularly Perturbed Generalized mKdV Equation with Higher-Degree Nonlinearities","display_name":"Periodic Traveling Wave Solutions of a Singularly Perturbed Generalized mKdV Equation with Higher-Degree Nonlinearities","publication_year":2025,"publication_date":"2025-12-13","ids":{"openalex":"https://openalex.org/W7115190868","doi":"https://doi.org/10.1142/s0218127426500392"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127426500392","doi":"https://doi.org/10.1142/s0218127426500392","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127426500392","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"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":"International Journal of Bifurcation and Chaos","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":null,"display_name":"Krishna Patra","orcid":"https://orcid.org/0009-0002-1831-4748","observed_orcids":["https://orcid.org/0009-0002-1831-4748"]},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"education","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Krishna Patra","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India"],"raw_orcid":"https://orcid.org/0009-0002-1831-4748","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India","institution_ids":["https://openalex.org/I24676775"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ch. Srinivasa Rao","orcid":"https://orcid.org/0000-0003-0701-3966","observed_orcids":["https://orcid.org/0000-0003-0701-3966"]},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"education","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ch. Srinivasa Rao","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India"],"raw_orcid":"https://orcid.org/0000-0003-0701-3966","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India","institution_ids":["https://openalex.org/I24676775"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I24676775"],"apc_list":null,"apc_paid":null,"fwci":0.8861,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.76320747,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"36","issue":"04","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":0.9404000043869019,"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":0.9404000043869019,"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":0.01640000008046627,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.016100000590085983,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/singularly-perturbed-problems","display_name":"singularly perturbed problems","score":0.8080000281333923},{"id":"https://openalex.org/keywords/abelian-integrals","display_name":"Abelian integrals","score":0.9340000152587891},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.49399998784065247}],"concepts":[{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.8307999968528748},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8080999851226807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6682999730110168},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6504999995231628},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.638700008392334},{"id":"https://openalex.org/C2993172089","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Periodic wave","level":3,"score":0.5774999856948853},{"id":"https://openalex.org/C2986045365","wikidata":"https://www.wikidata.org/wiki/Q1163350","display_name":"Wave speed","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2921999990940094},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.24220000207424164}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127426500392","doi":"https://doi.org/10.1142/s0218127426500392","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127426500392","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"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":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W175928657","https://openalex.org/W1480223776","https://openalex.org/W1979722387","https://openalex.org/W1979863106","https://openalex.org/W1980440330","https://openalex.org/W1996316724","https://openalex.org/W2001206262","https://openalex.org/W2005380085","https://openalex.org/W2014809428","https://openalex.org/W2016767879","https://openalex.org/W2022850134","https://openalex.org/W2026031976","https://openalex.org/W2028663304","https://openalex.org/W2028798193","https://openalex.org/W2036341165","https://openalex.org/W2073061323","https://openalex.org/W2090951893","https://openalex.org/W2094380752","https://openalex.org/W2313200692","https://openalex.org/W2507381567","https://openalex.org/W2738273254","https://openalex.org/W2780210009","https://openalex.org/W2801534390","https://openalex.org/W2964339755","https://openalex.org/W3020901533","https://openalex.org/W3081775939","https://openalex.org/W3088810264","https://openalex.org/W3161366195","https://openalex.org/W3201327641","https://openalex.org/W4225850556","https://openalex.org/W4293202503","https://openalex.org/W4313856280","https://openalex.org/W4367315970","https://openalex.org/W4400050895","https://openalex.org/W4401169615","https://openalex.org/W4406441152","https://openalex.org/W4409188329","https://openalex.org/W4413055697","https://openalex.org/W4413502844"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3],"investigate":[4],"the":[5,36,39,47,50,70],"existence":[6],"of":[7,27,38,41,49],"periodic":[8,28],"traveling":[9,29],"wave":[10,30,52],"solutions":[11,31],"for":[12],"a":[13,63],"singularly":[14],"perturbed":[15],"generalized":[16],"mKdV":[17],"(modified":[18],"Korteweg\u2013de":[19],"Vries)":[20],"equation":[21],"with":[22],"higher-degree":[23],"nonlinearities.":[24],"The":[25],"presence":[26],"is":[32,66],"demonstrated":[33],"by":[34],"utilizing":[35],"monotonicity":[37,48],"ratio":[40],"Abelian":[42],"integrals.":[43],"We":[44],"also":[45],"prove":[46],"limit":[51],"speed":[53],"and":[54,59],"further":[55],"derive":[56],"its":[57],"upper":[58],"lower":[60],"bounds.":[61],"Finally,":[62],"numerical":[64],"study":[65],"presented":[67],"to":[68],"illustrate":[69],"theoretical":[71],"results.":[72]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2025-12-15T00:00:00"}