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

This textbook introduces the well-posedness theory for initial-value problems of nonlinear,
dispersive partial differential equations, with special focus on two key models, the Korteweg …

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 …

1. Fourier multiplier, function space [symbol]. 1.1. Schwartz space, tempered distribution,
Fourier transform. 1.2. Fourier multiplier on L [symbol]. 1.3. Dyadic decomposition, Besov …

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 …

The nonlinear wave and Schrodinger equations on Euclidean space of any dimension, with
general power nonlinearity and with both the focusing and defocusing signs, are proved 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 …

On the local well-posedness of the Benjamin-Ono equation in Hs(R) Page 1 IMRN
International Mathematics Research Notices 2003, No. 26 On the Local Well-Posedness of …