Single soliton and double soliton solutions of the quadratic-nonlinear Korteweg-de Vries equation for small and long-times

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dc.authoridEsen, Alaattin/0000-0002-7927-5941
dc.authoridBashan, Ali/0000-0001-8500-493X
dc.authorwosidEsen, Alaattin/F-2415-2016
dc.authorwosidEsen, Alaattin/ABE-5694-2021
dc.authorwosidBashan, Ali/R-6644-2018
dc.contributor.authorBashan, Ali
dc.contributor.authorEsen, Alaattin
dc.date.accessioned2024-08-04T20:49:03Z
dc.date.available2024-08-04T20:49:03Z
dc.date.issued2021
dc.departmentİnönü Üniversitesien_US
dc.description.abstractIn this article, numerical solutions of the seven different forms of the single soliton and double soliton solutions of the Korteweg-de Vries equation are investigated. Since numerical solution of the six test problems for small-times do not exist in the literature, the present numerical results firstly are reported with exact solutions. Besides small-time solutions, long-time solutions of all test problems are obtained and compared with some of the earlier works. Present algorithm which is based on combination of finite difference method and differential quadrature method have obtained superior results than those in the given literature. Numerical and exact solutions for small-time of all test problems are plotted together for all test problems. Since the numerical results are too close to exact solutions the graphs are indistinguishable. Numerical simulations for long-time solutions are plotted and the error graphs are plotted for the end of the simulations of all test problems.en_US
dc.identifier.doi10.1002/num.22597
dc.identifier.endpage1582en_US
dc.identifier.issn0749-159X
dc.identifier.issn1098-2426
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85093530236en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage1561en_US
dc.identifier.urihttps://doi.org/10.1002/num.22597
dc.identifier.urihttps://hdl.handle.net/11616/99600
dc.identifier.volume37en_US
dc.identifier.wosWOS:000580649400001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherWileyen_US
dc.relation.ispartofNumerical Methods For Partial Differential Equationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectB-splineen_US
dc.subjectdifferential quadrature methoden_US
dc.subjectfinite difference methoden_US
dc.subjectKdV equationen_US
dc.subjectsolitonen_US
dc.titleSingle soliton and double soliton solutions of the quadratic-nonlinear Korteweg-de Vries equation for small and long-timesen_US
dc.typeArticleen_US

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