On the Exact Solution for Nonlinear Partial Differential Equations


MSc Student, School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran


In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equation (GEWE) which are the major soliton equations.


1. M. Abdur-Rab and J. Akhter, Sine-Function method in the soliton solution of nonlinear partial differential equations, GANIT: Journal of Bangladesh Mathematical Society, 32, 55-60 (2012).
2. G. Adomian, Solving Frontier Problem of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, MA (1994).
3. A.H.A. Ali, A.A. Soliman and K.R. Raslan, Soliton solution for nonlinear partial differential equations by using Cosine-Function method, Physics Letters Math., vol. 368, 299-304 (2007).
4. H.Z. Zedan and S.J. Monaaquel, The Sine-Cosine method For The Davey-Stewartson Equations, Appl. Math, 10, 103-111 (2010).