Among nonlinear PDEs, dispersive and wave equations form an important class of
equations. These include the nonlinear Schrodinger equation, the nonlinear wave equation …

This survey article is focused on two asymptotic models for internal waves, the Benjamin-
Ono (BO) and Intermediate Long Wave (ILW) equations that are integrable by inverse …

In part I of this work (Bona JL, Chen M and Saut JC 2002 Boussinesq equations and other
systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the …

Abstract The Benjamin–Ono equation is shown to be well-posed, both on the line and on the
circle, in the Sobolev spaces H s for s>− 1 2. The proof rests on a new gauge transformation …

We show that the Benjamin–Ono equation is globally well-posed in Hs (R) for s≥ 1. This is
despite the presence of the derivative in the nonlinearity, which causes the solution map to …

GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN LOW-REGULARITY
SPACES 1. Introduction In this paper we consider the Benj Page 1 JOURNAL OF THE …

This book provides a self-contained presentation of classical and new methods for studying
wave phenomena that are related to the existence and stability of solitary and periodic …

We show that the Cauchy problem for a class of dispersive perturbations of Burgers'
equations containing the low dispersion Benjamin–Ono equation∂ tu− D x α∂ xu=∂ x (u …

The aim of this paper is to show how a weakly dispersive perturbation of the inviscid Burgers
equation improves (enlarges) the space of resolution of the local Cauchy problem. More …

Nonlinear wave interactions for the Benjamin-Ono equation Page 1 IMRN International
Mathematics Research Notices 2005, No. 30 Nonlinear Wave Interactions for the Benjamin-Ono …