Since the 1980s, Fourier analysis methods have become of ever greater interest in the study
of linear and nonlinear partial differential equations. In particular, techniques based on …

A basic question in the theory of nonlinear partial differential equations is: when can a
singularity form and what is its nature? The typical well-posedness result (see eg [23]) …

The peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation
that is a model in shallow water theory and the theory of hyperelastic rods. We give a very …

Existence of permanent and breaking waves for a shallow water equation: a geometric
approach Page 1 ANNALES DE L’INSTITUT FOURIER ADRIAN CONSTANTIN Existence of …

This book is the written and somewhat expanded version of the author's lectures delivered at
the NSF-CBMS international research conference organized at the Mathematics Department …

This paper develops a new approach in the analysis of the Camassa–Holm equation. By
introducing a new set of independent and dependent variables, the equation is transformed …

On the scattering problem for the Camassa–Holm equation Page 1 10.1098/rspa.2000.0701 On
the scattering problem for the Camassa–Holm equation By Adrian Constantin† Department of …

We establish local well-posedness in the Sobolev space Hs with any s> 3 2 for an integrable
nonlinearly dispersive wave equation arising as a model for shallow water waves known as …

In the present paper, we use some standard a priori estimates for linear transport equations
to prove the existence and uniqueness of solutions for the Camassa-Holm equation with …

This paper is devoted to the continuation of solutions to the Camassa–Holm equation after
wave breaking. By introducing a new set of independent and dependent variables, the …