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...

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.

We investigate the well-posedness of a class of nonlinear dispersive waves on trees, in connection with the mathematical modeling of the human cardiovascular system. Specifically, we study the Benjamin-Bona-Mahony (BBM) equation, also known as the regularized long wave equation, posed on finite trees, together with standard junction and terminal boundary conditions. We prove that the Cauchy pro...

This paper discusses the existence and stability of solitary-wave solutions of a general higher-order Benjamin-Bona-Mahony (BBM) equation, which involves pseudo-differential operators for the linear part. One of such equations can be derived from water-wave problems as second-order approximate equations from fully nonlinear governing equations. Under some conditions on the symbols of pseudo-dif...

In this paper, the family of BBM equation with strong nonlinear dispersive B(m,n) equation is introduced. By using a simple and effective algebraic method ,some abundant exact solutions for this class of BBM equations are gotten and call its solutions with solitary patterns, solitary wave solution with singular point , smooth solitary wave solution , kink solution, antikink solution, floating s...

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...

The initialand boundary-value problem for the Benjamin-Bona-Mahony (BBM) equation is studied in this paper. The goal is to understand the periodic behavior (termed as eventual periodicity) of its solutions corresponding to periodic boundary condition or periodic forcing. To this aim, we derive a new formula representing solutions of this initialand boundary-value problem by inverting the operat...