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 …

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics is the first book to provide a systematic construction of exact …

In recent years, finding exact solutions to nonlinear differential equations has become a
fascinating study topic. In the present study, using the modified Kudryashov method and the …

Global Weak Solutions for a Shallow Water Equation Page 1 Commun. Math. Phys. 211, 45 –
61 (2000) Communications in Mathematical Physics © Springer-Verlag 2000 Global Weak …

Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …

An inverse scattering method is developed for the Camassa–Holm equation. As an
illustration of our approach the solutions corresponding to the reflectionless potentials are …

We use asymptotic analysis and a near-identity normal form transformation from water wave
theory to derive a 1+ 1 unidirectional nonlinear wave equation that combines the linear …

In this paper, we investigate the formation of singularities and the existence of peaked
traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The …

Traveling wave solutions of the Camassa–Holm equation Page 1 J. Differential Equations
217 (2005) 393–430 www.elsevier.com/locate/jde Traveling wave solutions of the Camassa–Holm …

This paper is concerned with several aspects of the existence of global solutions and the
formation of singularities for the Degasperis-Procesi equation on the line. Global strong …