The system is called a Benjamin-Ono-Boussinesq system because it can be reduced to a pair of equations whose linearization uncouples to a pair of linear Benjamin-Ono equations. Equations of type (1.1) are a class of essential model equations appearing in physics and fluid mechanics. To describe two-dimensional irrotational flows of an inviscid liquid in a uniform rectangular channel, Boussinesq...

We study persistence properties of solutions to some canonical dispersive models, namely the semi-linear Schrödinger equation, the k-generalized Korteweg-de Vries equation and the Benjamin-Ono equation, in weighted Sobolev spaces Hs(Rn) ∩ L2(|x|ldx), s, l > 0.

Two-dimensional nonlinear models are developed to account for abnormal surface ocean waves generation and propagation. These models are based on the KadomtsevPetviashvili equation, the 2D Benjamin-Ono equation and the 2D Gardner equation. Possible mechanisms of the waves formation suggested are the resonant interaction between semi-plane waves or waves with curved fronts or the transverse insta...

It was proved by Linares and Ortega in [24] that the linearized Benjamin-Ono equation posed on a periodic domain T with a distributed control supported on an arbitrary subdomain is exactly controllable and exponentially stabilizable. The aim of this paper is to extend those results to the full Benjamin-Ono equation. A feedback law in the form of a localized damping is incorporated in the equati...

An alternative type of nonlinear evolution equation is derived that describes interfacial waves in a two-layer fiuid system. The equation presented here is a higher-order version of the Benjamin-Ono (BO) equation. A solitary-wave solution of the equation is obtained by means of a singular perturbation method. The characteristics of the solution are discussed in comparison with those for a highe...

— In this paper we construct a Gibbs measure for the derivative Schrödinger equation on the circle. The construction uses some renormalisations of Gaussian series and Wiener chaos estimates, ideas which have already been used by the second author in a work on the Benjamin-Ono equation.