# HOP

## Seminar

### Asymptotics for the Camassa-Holm equation

Seminar Room 1, Newton Institute

#### Abstract

I will present recent results on asymptotic behaviors for the Ca-massa–Holm (CH) equation ut - utxx + 2?ux + 3uux = 2uxuxx + uuxxx on the line, ? being a nonnegative parameter.

Firstly, I will describe the long-time asymptotic behavior of the solution u? (x, t), ? > 0 of the initial-value problem with fast decaying initial data u0(x). It appears that u? (x, t) behaves differently in different sectors of the (x, t)-half-plane. Then I will analyse the behavior of u? (x, t) as ? 0.

The methods are inverse scattering in a matrix Riemann-Hilbert approach and Deift and Zhou’s nonlinear steepest descent method.

Work in collaboration with Dmitry Shepelsky.

## Comments

Start the discussion!