Riemann--Hilbert problem for Camassa--Holm equation with step-like initial data

Alexander Minakov

Published 2014-01-27, updated 2014-04-12Version 2

The Cauchy problem for the Camassa -- Holm equation with step-like initial conditions is reformulated as a Riemann -- Hilbert problem. The the initial value problem solution is obtained then in a parametric form from the Riemann -- Hilbert problem solution.