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...

The system is called a Benjamin-Ono-Boussinesq system because it can be reduced to a pair of equations whose linearization uncouples to a pair of linear Benjamin-Ono equations. Equations of type (1.1) are a class of essential model equations appearing in physics and fluid mechanics. To describe two-dimensional irrotational flows of an inviscid liquid in a uniform rectangular channel, Boussinesq...

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...

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.