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

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.