Traveling wave solutions of the BBM-like equations

Abstract

In this work, we apply the factorization technique to the Benjamin–Bona–Mahony-like equations, B(m, n), in order to get traveling wave solutions. We will focus on some special cases for which m ≠ n, and we will obtain these solutions in terms of the special forms of Weierstrass functions.

The Traveling Wave Solutions and Their Bifurcations for the BBM-LikeB(m,n)Equations

“…By using four different ansatzs, they obtained some exact solutions such as compactons, solitary pattern solutions, solitons, and periodic solutions. Kuru [22][23][24] considered the following BBM-like equations with a fully nonlinear dispersive term:…”

“…Completing the integrals in the two equations above and noting that = ( ), we obtain 9 ( ) and 10 ( ) as (23) and (24). (5) When > and 0 < , Γ 5 has the expression…”

Traveling Wave Solutions of the Benjamin-Bona-Mahony Water Wave Equations

“…To obtain the traveling wave solutions to these nonlinear evolution equations, many methods were attempted, such as the inverse scattering method [5], Hirotas bilinear transformation [6], the tanhsech method, extended tanh method, sine-cosine method [7], homogeneous balance method, Bäcklund transformation [8], the theory of Weierstrass elliptic function method [9], the factorization technique [10,11], the Wadati trace method, pseudospectral method, Exp-function method, and the Riccati equation expansion method were used to investigate these types of equations [12,13]. The above methods derived many types of solutions from most nonlinear evolution equations [14].…”