Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications

Nikolay K. Vitanov, Zlatinka I. Dimitrova and Kaloyan N. Vitanov

Applied Mathematics and Computation, 2015, vol. 269, issue C, 363-378

Abstract: We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use differential equation for a special function that contains as particular cases trigonometric and hyperbolic functions as well as the elliptic function of Weierstrass and Jacobi. We show that for this case the studied class of nonlinear partial differential equations can be reduced to a system of two equations containing polynomials of the unknown functions. This system may be further reduced to a system of nonlinear algebraic equations for the parameters of the solved equation and parameters of the solution. Any nontrivial solution of the last system leads to a traveling wave solution of the solved nonlinear partial differential equation. The methodology is illustrated by obtaining solitary wave solutions for the generalized Korteweg–deVries equation and by obtaining solutions of the higher order Korteweg–deVries equation.

Keywords: Method of simplest equation; Nonlinear partial differential equations; Exact solutions (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:269:y:2015:i:c:p:363-378

DOI: 10.1016/j.amc.2015.07.060

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