Benjamin--Ono Soliton Dynamics in a Slowly Varying Potential Revisited

Multiple Soliton Solutions of Second-order Benjamin-ono Equation

We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of Multiple soliton solutions of secondorder Benjamin-Ono equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

Soliton Interaction with Slowly Varying Potentials

We study the Gross-Pitaevskii equation with a slowly varying smooth potential, V (x) = W (hx). We show that up to time log(1/h)/h and errors of size h in H, the solution is a soliton evolving according to the classical dynamics of a natural effective Hamiltonian, (ξ + sech ∗ V (x))/2. This provides an improvement (h→ h) compared to previous works, and is strikingly confirmed by numerical simula...

Benjamin-Ono Equation on a Half-Line

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...

The Cauchy problem for the Benjamin-Ono equation in L2 revisited

In a recent work [12], Ionescu and Kenig proved that the Cauchy problem associated to the Benjamin-Ono equation is well-posed in L(R). In this paper we give a simpler proof of Ionescu and Kenig’s result, which moreover provides stronger uniqueness results. In particular, we prove unconditional well-posedness in Hs(R), for s > 1 4 .