Article ID Journal Published Year Pages File Type
5775655 Applied Mathematics and Computation 2017 9 Pages PDF
Abstract
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 fξ2=n2(f2−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.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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