Exploring the influence of layer and neuron configurations on Boussinesq equation solutions via a bilinear neural network framework

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dc.contributor.authorIsah, Muhammad Abubakar
dc.contributor.authorYokus, Asif
dc.contributor.authorKaya, Doğan
dc.date.accessioned2024-05-29T09:03:50Z
dc.date.available2024-05-29T09:03:50Z
dc.date.issued2024en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractThis study examines the Boussinesq equation, which is a nonlinear partial differential equation used to describe long wave propagation in shallow water and has broader applications, including nonlinear lattice waves, vibrations in nonlinear strings, and ion sound waves in plasma. The Boussinesq equation provides an insight into the nonlinear long wave propagation behavior in shallow water by taking wave phase into account. Its versatility extends its utility beyond fluid dynamics to various physical phenomena. By providing specific activation functions in the ``2-3-1?? and ``2-5-1?? neural network models, respectively, the generalized lump solution and the precise analytical solutions are produced using the bilinear neural network approach. These analytical solutions, together with the related rogue waves, dark soliton, and bright soliton, are derived using symbolic computation. These findings fill in the gaps in the current research about the Boussinesq equation. The dynamical properties of these waves are displayed on three-dimensional, contour, density, and two-dimensional graphs. The response of the wave solution to different values of wave speed in relation to the wave phase it contains has been described with the help of wave intensity. In addition, the advantages and disadvantages of the layers used in the analytical technique to generate solutions have been discussed. The efficient techniques employed in this research are useful for studying the nonlinear differential equations in one-dimensional nonlinear lattice waves, vibrations in a nonlinear string, and ion sound waves in plasma.en_US
dc.identifier.doi10.1007/s11071-024-09708-3en_US
dc.identifier.scopus2-s2.0-85193731390en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.urihttps://hdl.handle.net/11467/7292
dc.identifier.urihttps://doi.org/10.1007/s11071-024-09708-3
dc.identifier.wosWOS:001228800100001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringer Science and Business Media B.V.en_US
dc.relation.ispartofNonlinear Dynamicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/embargoedAccessen_US
dc.subjectBilinear neural network method; The Boussinesq equation; Rogue waves; Hirota bilinear formen_US
dc.titleExploring the influence of layer and neuron configurations on Boussinesq equation solutions via a bilinear neural network frameworken_US
dc.typeArticleen_US

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