in this article, the modified exp-function method is used to construct many exact solutions to the nonlineargeneralized k(n,n) and bbm equations with variable coefficients. under different parameter conditions, explicitformulas for some new exact solutions are successfully obtained. the proposed solutions are found to beimportant for the explanation of some practical physical problems.

In this paper, based on the homogeneous balance principle and two improved projective Riccati Equations, exact solutions to the general form of BBM equation and the generalized BBM-Burgers equation with nonlinear terms of any order are obtained, which include several kinds of solitary wave solutions and periodic wave solutions. Some of them are found for the first time.

An approach is proposed to obtain some exact explicit solutions in terms of the Weierstrass’ elliptic function ℘ to a generalized Benjamin-Bona-Mahony (BBM) equation. Conditions for periodic and solitary wave like solutions can be expressed compactly in terms of the invariants of ℘. The approach unifies recently established ad-hoc methods to a certain extent. Evaluation of a balancing principle...

An auxiliary equation technique is applied to investigate a generalized Benjamin-Bona-Mahony equation with variable coefficients. Many exact traveling wave solutions are obtained which include algebraic solutions, solitons, solitary wave solutions and trigonometric solutions. Mathematics Subject Classification: 35Q53, 35B35

In this paper, we investigate the first integral method for solving the generalized Benjamin-BonaMahony (BBM) equation. This idea can obtain some exact solutions of this equations based on the theory of Commutative algebra.

We consider the Benjamin-Bona-Mahony (BBM) equation on the one dimensional torus T = R/(2πZ). We prove a Unique Continuation Property (UCP) for small data in H(T) with nonnegative zero means. Next we extend the UCP to certain BBM-like equations, including the equal width wave equation and the KdV-BBM equation. Applications to the stabilization of the above equations are given. In particular, we...