Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 30, No 1, (2019), 29p-42p
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  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.