{"id":"https://openalex.org/W7213497484","doi":"https://doi.org/10.48550/arxiv.2609.18625","title":"Existence of multi-solitons for logarithmic Schr{\u00f6}dinger equation with a perturbation of a smooth $L^2$-subcritical function nonlinearity","display_name":"Existence of multi-solitons for logarithmic Schr{\u00f6}dinger equation with a perturbation of a smooth $L^2$-subcritical function nonlinearity","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213497484","doi":"https://doi.org/10.48550/arxiv.2609.18625"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18625","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18625","pdf_url":"https://arxiv.org/pdf/2609.18625","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.18625","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120668736","display_name":"Mohamed Bensaid","orcid":"https://orcid.org/0009-0009-1598-8203","observed_orcids":["https://orcid.org/0009-0009-1598-8203"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bensaid, Mohamed","raw_affiliation_strings":["LPP, Paradyse"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LPP, Paradyse","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5120668736"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994999766349792,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/logarithmic-schrodinger-equation","display_name":"logarithmic Schr\u00f6dinger equation","score":0.9120000004768372},{"id":"https://openalex.org/keywords/multi-soliton-solutions","display_name":"N-soliton solutions","score":0.8159999847412109},{"id":"https://openalex.org/keywords/soliton-solutions","display_name":"soliton solutions","score":0.7910000085830688},{"id":"https://openalex.org/keywords/focusing-nonlinearity","display_name":"focusing nonlinearity","score":0.8510000109672546},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.6980000138282776},{"id":"https://openalex.org/keywords/iterative-construction","display_name":"iterative construction","score":0.7730000019073486},{"id":"https://openalex.org/keywords/nonlinear-schrodinger-equation","display_name":"nonlinear Schr\u00f6dinger equation","score":0.9350000023841858}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6509000062942505},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.640500009059906},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6309999823570251},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6223000288009644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6067000031471252},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5042999982833862},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3684999942779541},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.3553999960422516},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3499999940395355},{"id":"https://openalex.org/C174256460","wikidata":"https://www.wikidata.org/wiki/Q911364","display_name":"Perturbation theory (quantum mechanics)","level":2,"score":0.3287000060081482},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.32710000872612},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C153359094","wikidata":"https://www.wikidata.org/wiki/Q7207873","display_name":"Poincar\u00e9\u2013Lindstedt method","level":3,"score":0.31060001254081726},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27300000190734863}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.18625","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18625","pdf_url":"https://arxiv.org/pdf/2609.18625","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05749149v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05749149","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.18625","doi":"https://doi.org/10.48550/arxiv.2609.18625","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18625","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.18625","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18625","pdf_url":"https://arxiv.org/pdf/2609.18625","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5016747878","display_name":null,"funder_award_id":"R-CDP-24-004-C2EMPI","funder_id":"https://openalex.org/F4320316137","funder_display_name":"Universit\u00e9 de Lille"}],"funders":[{"id":"https://openalex.org/F4320316137","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213497484.pdf","grobid_xml":"https://content.openalex.org/works/W7213497484.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1964470050","https://openalex.org/W1991440858","https://openalex.org/W2000258892","https://openalex.org/W2005105370","https://openalex.org/W2042754533","https://openalex.org/W2054531633","https://openalex.org/W2071132730","https://openalex.org/W2081418818","https://openalex.org/W2312961750","https://openalex.org/W2563583896","https://openalex.org/W2980337949","https://openalex.org/W3010504177","https://openalex.org/W4399177674","https://openalex.org/W4400018653","https://openalex.org/W4409046519","https://openalex.org/W4410530611"],"related_works":["https://openalex.org/W4409916035","https://openalex.org/W4298072395","https://openalex.org/W3010504177","https://openalex.org/W1493897935","https://openalex.org/W7080124082","https://openalex.org/W4414694508","https://openalex.org/W2558445285","https://openalex.org/W3132341067","https://openalex.org/W3168442632","https://openalex.org/W2054531633"],"abstract_inverted_index":{"In":[0],"this":[1,32],"paper,":[2],"we":[3],"study":[4],"the":[5,26,43,67,71],"nonlinear":[6],"Schr{\u00f6}dinger":[7],"equation":[8],"with":[9,49,61],"a":[10,13,18],"nonlinearity":[11],"combining":[12],"focusing":[14],"logarithmic":[15],"term":[16],"and":[17],"smooth":[19],"$L^2$-subcritical":[20],"function.":[21],"Our":[22],"main":[23],"result":[24],"is":[25],"construction":[27,58],"of":[28,45,70],"multisoliton":[29],"solutions":[30],"for":[31,39],"equation.":[33],"These":[34],"special":[35],"configurations":[36],"behave":[37],"asymptotically,":[38],"large":[40],"times,":[41],"as":[42],"superposition":[44],"several":[46],"solitons":[47],"moving":[48],"distinct":[50],"velocities.":[51],"The":[52],"proof":[53],"relies":[54],"on":[55],"an":[56],"iterative":[57],"method":[59],"combined":[60],"localized":[62],"energy":[63],"estimates":[64],"adapted":[65],"to":[66],"mixed":[68],"structure":[69],"nonlinearity.":[72]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-18T00:00:00"}
