Analytical approximate solutions for nonplanar Burgers equations by weighted residual method

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dc.authorid0000-0001-8590-3396
dc.authorid0000-0001-7266-1893
dc.contributor.authorDemiray, Hilmien_US
dc.contributor.authorEl-Zahar, Essam Roshdyen_US
dc.date.accessioned2020-09-07T11:08:33Z
dc.date.available2020-09-07T11:08:33Z
dc.date.issued2020-08-13
dc.departmentIşık Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümüen_US
dc.departmentIşık University, Faculty of Arts and Sciences, Department of Mathematicsen_US
dc.description.abstractIn this work, analytical approximate progressive wave solutions for the generalized form of the nonplanar KdV-Burgers (KdV-B) and mKdV-Burgers (mKdV-B) equations are presented and the results are discussed. Motivated with the exact solutions of the planar KdV-B and mKdV-B equations, the weighted residual method is applied to propose analytical approximate solutions for the generalized form of the nonplanar KdV-B and mKdV-B equations. The structure of the KdV-B equation assumes a solitary wave type of solution, whereas the mKdV-B equation assumes a shock wave type of solution. The analytical approximate progressive wave solutions for the cylindrical(spherical) KdV-B and mKdV-B equations are obtained as some special cases and compared with numerical solutions and the results are depicted on 2D and 3D figures. The results revealed that both solutions are in good agreement. The advantage of the present method is that it is rather simple as compared to the inverse scattering method and gives the same results with the perturbative inverse scattering technique. Moreover, the present analytical solutions allow readers to carry out physical parametric studies on the behavior of the solution. In addition to the present solutions are defined overall the problem domain not only over the grid points, as well as the solution calculation has less CPU time-consuming and round-off error.en_US
dc.description.versionPublisher's Versionen_US
dc.identifier.citationEl-Zahar, E. R. & Demiray, H. (2020). Analytical approximate solutions for nonplanar Burgers equations by weighted residual method. Results in Physics, 18, 1-8. doi:10.1016/j.rinp.2020.103293en_US
dc.identifier.doi10.1016/j.rinp.2020.103293
dc.identifier.endpage8
dc.identifier.issn2211-3797
dc.identifier.scopus2-s2.0-85089472297
dc.identifier.scopusqualityQ2
dc.identifier.startpage1
dc.identifier.urihttps://hdl.handle.net/11729/2372
dc.identifier.urihttp://dx.doi.org/10.1016/j.rinp.2020.103293
dc.identifier.volume18
dc.identifier.wosWOS:000577353600006
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakScience Citation Index Expanded (SCI-EXPANDED)en_US
dc.institutionauthorDemiray, Hilmien_US
dc.institutionauthorid0000-0001-8590-3396
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.publisherElsevier B.V.en_US
dc.relation.ispartofResults in Physicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectDusty plasmasen_US
dc.subjectIon acoustic wavesen_US
dc.subjectLighthill methoden_US
dc.subjectAnalytical approximate wave solutionen_US
dc.subjectNonplanar KdV-B and mKdV-B equationsen_US
dc.subjectWeighted residual methoden_US
dc.titleAnalytical approximate solutions for nonplanar Burgers equations by weighted residual methoden_US
dc.typeArticleen_US
dspace.entity.typePublication

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