This note proves the orbital stability in the energy space H of the sum of widelyspaced 1-solitons for the Benjamin-Ono equation, with speeds arranged so as to avoid collisions.

Computation of solitons of the cubically-nonlinear Benjamin–Ono equation is challenging. First, the equation contains the Hilbert transform, a nonlocal integral operator. Second, its solitary waves decay only as O(1/jxj). To solve the integro-differential equation for waves traveling at a phase speed c, we introduced the artificial homotopy H(uXX) c u + (1 d)u + du = 0, d 2 [0,1] and solved it ...

In this paper we study local well-posedness in the energy space for a family of dispersive equations that can be seen as dispersive " interpolations " between the KdV and the Benjamin-Ono equation.

We consider a two-dimensional generalization of the Benjamin-Ono equation and prove that it admits solitary-wave solutions that are analytic functions. We find the optimal decay rate at infinity of these solitary waves.

This paper discusses the existence and uniqueness of the generalized solution in the sense of Colombeau to the Benjamin-Ono (B-O) equation and the relationship between the new generalized solution and the classical solution.

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...