Stability of Deep Water Waves Governed by the Benjamin-Ono Equation

Solitary waves of the rotation-generalized Benjamin-Ono equation

This work studies the rotation-generalized Benjamin-Ono equation which is derived from the theory of weakly nonlinear long surface and internal waves in deep water under the presence of rotation. It is shown that the solitary-wave solutions are orbitally stable for certain wave speeds.

Asymptotic stability of solitons for the Benjamin-Ono equation

In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of [16], [18]. As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.

Perturbation theory for the Benjamin–Ono equation

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...

Benjamin-Ono Equation on a Half-Line

On the existence, regularity and decay of solitary waves to a generalized 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.