We prove the local well posedness of the Benjamin-Ono equation and the generalized Benjamin-Ono equation in H(T). This leads to a global wellposedness result in H(T) for the Benjamin-Ono equation.

We study the interaction of suitable small and high frequency waves evolving by the flow of the Benjamin-Ono equation. As a consequence, we prove that the flow map of the Benjamin-Ono equation can not be uniformly continuous on bounded sets of H s (R) for s > 0.

We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analogue of BenjaminOno equation. The latter is known to describe internal waves o...

in recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. one such method is known as the new extended (g'/g)-expansion method and was proposed by roshid et al. in this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (nlpdes), namely the benjamin-ono equation. it i...

We develop a perturbation theory for the Benjamin–Ono (BO) equation. This perturbation theory is based on the inverse scattering transform for the BO equation, which was originally developed by Fokas and Ablowitz and recently refined by Kaup and Matsuno. We find the expressions for the variations of the scattering data with respect to the potential, as well as the dual expression for the variat...

We prove that the Benjamin-Ono equation is well-posed in H(T). This leads to a global well-posedeness result in H(T) thanks to the energy conservation. Résumé. Nous montrons que l’équation de Benjamin-Ono est bien posée dans H(T). Il découle alors de la conservation de l’énergie que la solution existe pour tout temps dans cette espace.

In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation suc...

The interacting soliton equation of the Benjamin-Ono equation is found to be st = Hsxx − csx − isxH(s−1sx) − is−1sxH(sx), where H is the Hilbert transform. It is integrable in the sense that it has infinitely many commuting symmetries and conservation laws in involution. Only solitons with speed specified by the spectral parameter c emerge from its time evolution. Since it is connected to the B...