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...

Abstract In this note we study the controllability of the Generalized BenjaminBona-Mahony equation (BBM) with homogeneous Dirichlet boundary conditions. Under some conditions we shall prove the system is approximately controllable on [0, t1] if and only if the following algebraic condition holds Rank[Bj ] = γj , where Bj acts from IR m to R(Ej), λj ’ s are the eigenvalues of −∆ with Dirichlet b...

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...

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...