The effect of weak lateral dispersion of Zakharov-Kutznetsov-type on a Benjamin-Ono solitary wave is studied both asymptotically and numerically. The asymptotic solution is based on an approximate variational solution for the solitary wave, which is then modulated in time through the use of conservation equations. The effect of the dispersive radiation shed as the solitary wave evolves is also ...

We establish the local well-posedness of the generalized BenjaminOno equation ∂tu+H∂ xu±u ∂xu = 0 in Hs(R), s > 1/2−1/k for k ≥ 12 and without smallness assumption on the initial data. The condition s > 1/2−1/k is known to be sharp since the solution map u0 7→ u is not of class Ck+1 on Hs(R) for s < 1/2 − 1/k. On the other hand, in the particular case of the cubic Benjamin-Ono equation, we prov...

For initial data in Sobolev spaces H s ( T ) , 1 2 < ? the solution to Cauchy problem for Benjamin-Ono equation on circle is shown grow at most polynomially time a rate + t 3 ? ? 0 ? . The key establishing this result discovery of nonlinear smoothing effect equation, according which satisfied by certain gauge transform, widely used well-posedness theory problem, becomes smoother once its free r...

In this paper we prove that the Benjamin–Ono equation admits an analytic Birkhoff normal form in open neighborhood of zero H0s(T,R) for any s>−1/2 where denotes subspace Sobolev space Hs(T,R) elements with mean 0. As application show −1/2<s<0, flow map S0t:H0s(T,R)→H0s(T,R) is nowhere locally uniformly continuous a H0s(T,R).

In this work we continue our study initiated in [10] on the uniqueness properties of real solutions to the IVP associated to the Benjamin-Ono (BO) equation. In particular, we shall show that the uniqueness results established in [10] do not extend to any pair of non-vanishing solutions of the BO equation. Also, we shall prove that the uniqueness result established in [10] under a hypothesis inv...