KAM Tori for generalized Benjamin-Ono equation

Solitary waves of the rotation-generalized Benjamin-Ono equation

This work studies the rotation-generalized Benjamin-Ono equation which is derived from the theory of weakly nonlinear long surface and internal waves in deep water under the presence of rotation. It is shown that the solitary-wave solutions are orbitally stable for certain wave speeds.

Singularity Formation in the Generalized Benjamin-ono Equation

A Fourier-collocation scheme is used to approximate solutions to the generalized Benjamin-Ono equation ut +uux −Huxx = 0. The numerical simulation suggests that the equation features smooth solutions that become unbounded in finite time.

Perturbation theory for the Benjamin–Ono equation

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...

Benjamin-Ono Equation on a Half-Line

Sharp ill-posedness result for the periodic Benjamin-Ono equation

We prove the discontinuity for the weak L(T)-topology of the flowmap associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in Hs(T) as soon as s < 0 and thus completes exactly the well-posedness result obtained in [12]. AMS Subject Classification : 35B20, 35Q53.