We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usuall...

We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the ODE’s which correspond to the projection of the Benjamin-Ono equation, posed on the circle, on the first N , N ≥ 1 modes in the trigonometric bases.

Here we continue the study of the initial value problem for the third order Benjamin-Ono equation in the weighted Sobolev spaces Hs γ = H s⋂L2γ , where s > 3, γ ≥ 0. The result is the proof of well-posedness of the afore mentioned problem in Hs γ , s > 3, γ ∈ [0, 1]. The proof involves the use of parabolic regularization, the Riesz-Thorin interpolation theorem and the construction technique of ...

A priori estimates and existence of real-valued periodic solutions to the modified Benjamin-Ono equation with initial data in $H^s$ for $s>1/4$ are proved locally time. The approach relies on frequency dependent time localization, after which dispersive properties from Euclidean space recovered. same regularity results cubic derivative nonlinear Schr\"odinger equation.

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usuall...

In this paper, we survey our recent results on the Benjamin–Ono equation torus. As an application of methods developed construct large families periodic or quasiperiodic solutions, which are not $C^\\infty$-smooth

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...