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 obtain conservation laws at negative regularity for the Benjamin-Ono equation on line and circle. These conserved quantities control $H^s$ norm of solution $-\frac{1}{2} < s 0$. The are obtained from a study perturbation determinant associated to Lax pair equation.

We study the initial value problem associated to the dispersion generalized Benjamin-Ono equation. Our aim is to establish well posedness results in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model. RÉSUMÉ. Nous étudions le problème de Cauc...

whereH is the Hilbert transform operator defined (on the spaces C(R : H), σ ∈ R) by the Fourier multiplier −i sgn(ξ). The Benjamin–Ono equation is a model for one-dimensional long waves in deep stratified fluids ([1] and [16]) and is completely integrable. The initial-value problem for this equation has been studied extensively for data in the Sobolev spaces H r (R), σ ≥ 0. It is known that the...