The Handbook of Nonlinear Partial Differential Equations is the latest in a series of
acclaimed handbooks by these authors and presents exact solutions of more than 1600 …

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 …

In recent years two nonlinear dispersive partial differential equations have attracted much
attention due to their integrable structure. We prove that both equations arise in the …

In this work, we employ the∂¯-steepest descent method to investigate the Cauchy problem
of the complex short pulse (CSP) equation with initial conditions in weighted Sobolev space …

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 …

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 this paper we first describe the current method for obtaining the Camassa–Holm equation
in the context of water waves; this requires a detour via the Green–Naghdi model equations …

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 …