Open AccessSimple equation method for nonlinear partial differential equations and its applications
Author(s) -
Taher A. Nofal
Publication year - 2016
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2015.05.006
Subject(s) - riccati equation , mathematics , first order partial differential equation , partial differential equation , bernoulli differential equation , fisher's equation , nonlinear system , differential equation , kadomtsev–petviashvili equation , simple (philosophy) , independent equation , burgers' equation , integro differential equation , exact differential equation , bernoulli's principle , mathematical analysis , hyperbolic partial differential equation , separable partial differential equation , characteristic equation , ordinary differential equation , differential algebraic equation , physics , philosophy , epistemology , quantum mechanics , thermodynamics
In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs) such as, Kodomtsev–Petviashvili (KP) equation, the (2+1)-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems