Asymptotic stability of solitons for the Benjamin-Ono equation

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.

Stability in H of the sum of K solitons for the Benjamin-Ono equation

This note proves the orbital stability in the energy space H of the sum of widelyspaced 1-solitons for the Benjamin-Ono equation, with speeds arranged so as to avoid collisions.

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

Temporal Asymptotic Behavior of Solutions of the Benjamin-ono-burgers Equation

We study certain similarity solutions of the Benjamin-Ono-Burgers (BOB) equation and their role in the asymptotic behavior of the general solution. For small initial data in L 1 (R) we prove that a solution of the BOB equation exists in BC(R + ; L 1 (R)) and depends continuously on its initial data. Results about existence, uniqueness, regularity, and spatial asymptotics of solutions of a simil...