Abstract
The F-expansion method is used to find traveling wave solutions to various wave equations. By giving more solutions of the general subequation, an extended F-expansion method is introduced by Emmanuel. In our work, a generalized KdV type equation of neglecting the highest-order infinitesimal term, which is an important water wave model, is discussed by using the extended F-expansion method. And when the parameters satisfy certain relations, some new exact solutions expressed by Jacobi elliptic function, hyperbolic function, and trigonometric function are obtained. The related results are enriched.
Highlights
It has recently become more interesting to obtain exact solutions of nonlinear partial differential equations
A lot of physical models have supported a wide variety of solitary wave solutions
Much effort has been spent on this task and many significant methods have been established such as inverse scattering transform [1], Backlund and Darboux transform [2], Hirota [3], homogeneous balance method [4], Jacobi elliptic function method [5], tanh-function method [6], exp-function method [7], simple equation method [8], F-expansion method [9, 10], improved F-expansion method [11], and extended F-expansion method [12]
Summary
It has recently become more interesting to obtain exact solutions of nonlinear partial differential equations. We apply the extended F-expansion method on a higher-order wave equation of KdV type for obtaining new exact traveling solutions. Neglecting two high-order infinitesimal terms of O(α3, α2β), (1) can be reduced to another high-order wave equation of KdV type [18, 19] as follows: ηt + ηx + αηηx + βηxxx + ρ1α2η2ηx (4). If only we neglect the highest-order infinitesimal term of O(α2β), (1) can be reduced to a new generalized KdV equation as follows: ηt + ηx + αηηx + βηxxx + ρ1α2η2ηx (5). In this paper, regarding the ρi (i = 1, 2, 3, 4) as free parameters and by using the extended F-expansion method [12], we will investigate exact traveling wave solutions of (5).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
