Analytical methods and Riccati neural networks method of Kudryashov’s quintuple self-phase modulation with dual-form of generalized nonlocal nonlinearity
SCIENTIFIC REPORTS, cilt.2026, ss.1-32, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 2026
- Basım Tarihi: 2026
- Doi Numarası: 10.1038/s41598-026-50283-x
- Dergi Adı: SCIENTIFIC REPORTS
- Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), BIOSIS, Chemical Abstracts Core, MEDLINE, Directory of Open Access Journals
- Sayfa Sayıları: ss.1-32
- Erciyes Üniversitesi Adresli: Evet
Özet
KABUL EDİLDİ
In thispaper,theexactsolitonsolutionsofthenonlinearSchr¨odinger’sequationhavingKudryashov’squintuple
powerlawofrefractiveindextogetherwithdualformofgeneralizednonlocalnonlinearityarestudied.Thepro-
posedsystemisanon-integrableequation.Riccatisubequationtechniquebasedontheneuralnetworkmodelis
considered. TheRiccatisubequationneuralnetworksmodelasactivationfunctionsinthefirsthiddenlayerof
the neuralnetworkarchitecturetoreachtooutputasanexactsolutionistaken.Thediverseformsofsolitary
wavesolutionsbyutilizingtheimprovedtan(ϕ/2)-expansion techniqueandtheexp(−ϕ(η))-Expansion scheme
are delivered.Inparticular,thekeytypesfound(e.g.,darksolitons,singularsolitons,combinedhyperbolic
function solutions).Toachievethis,anillustrativeexampleoftheSchr¨odinger’sequationisprovidedtodemon-
strate thefeasibilityandreliabilityoftheprocedurewhichusedinthisstudy.Theeffectofthefreeparameters
on thebehaviorofacquiredfigurestoafewobtainedsolutionsfortwocasesofrationalexactsolutionsare
also analyzedduetothenatureofnonlinearities.Thedynamicpropertiesoftheobtainedresultsareshown
and analyzedbysomedensity,twoandthree-dimensionalimages.Theresultsmayprovideafurtherdetailed
physicalunderstandingofnonlinearplasmawaveinteractions,contributingtothedevelopmentofadvanced
modelsforhigh-energyplasmawavemodulation,energytransport,andopticalsolitons.