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...

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.

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 paper, we prove that the Cauchy problem associated to the following higher-order Benjamin-Ono equation (0.1) ∂tv − bH∂ 2 x v − aǫ∂ x v = cv∂xv − dǫ∂x(vH∂xv +H(v∂xv)), is globally well-posed in the energy space H(R). Moreover, we study the limit behavior when the small positive parameter ǫ tends to zero and show that, under a condition on the coefficients a, b, c and d, the solution vǫ t...

Abstract We present new soliton equations related to the A -type spin Calogero–Moser (CM) systems introduced by Gibbons and Hermsen. These are generalizations of Benjamin–Ono (BO) equation recently non-chiral intermediate long-wave (ncILW) equation. obtain multi-soliton solutions these BO ncILW via a spin-pole ansatz where dynamics is governed CM system in rational hyperbolic cases, respectivel...