Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/3610

 Title: Recent Developments of the Methodology of the Modified Method of Simplest Equation with Application Authors: Vitanov, Nikolay K. Keywords: nolninear partial differential equationsexact analytical solutionsmodified method of simplest equation Issue Date: 2019 Publisher: Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences Citation: Pliska Studia Mathematica Bulgarica, Vol. 30, No 1, (2019), 29p-42p Abstract: We discuss an extension of the modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations. The extension includes the possibility for use of: (i) more than one simplest equation; (ii) relationship that contains as particular cases the relationship used by Hirota [1] and the relationship used in the previous version of the methodology; (iii) transformation of the solution that contains as particular case the possibility of use of the Painleve expansion; (iv) more than one balance equation. The discussed version of the methodology allows: obtaining multi-soliton solutions of nonlinear partial differential equations if such solutions do exist and obtaining particular solutions of nonintegrable nonlinear partial differential equations. Examples for the application of the methodology are discussed. 2010 Mathematics Subject Classification: 35E20. Description: [Vitanov Nikolay K.; Витанов Николай К.] URI: http://hdl.handle.net/10525/3610 ISSN: 0204-9805 Appears in Collections: 2019 Volume 30

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