On solitary wave solutions of a class of nonlinear partial differential equations based on the function 1/cosh(n)(alpha x plus beta t)

The method of simplest equation is applied for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. The used simplest equation is f xi(2) = n(2) (f(2) - f((2n+2)/n)). The developed methodology is illustrated on examples of classes of nonlinear partial differential equations that contain: (i) only monomials of odd grade with respect to participating derivatives; (ii) only monomials of even grade with respect to participating derivatives; (iii) monomials of odd and monomials of even grades with respect to participating derivatives. The obtained solitary wave solution for the case (i) contains as particular cases the solitary wave solutions of Korteweg-devries equation and of a version of the modified Korteweg-devries equation. One of the obtained solitary wave solutions for the case (ii) is a solitary wave solution of the classic version of the Boussinesq-type equation. (C) 2017 Elsevier Inc. All rights reserved