Long time asymptotics of the Camassa–Holm equation on the half-line

We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation u t - u t x x + 2 u x + 3 u u x = 2 u x u x x + u u x x x on the half-line x ≥ 0 . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane x > 0 , t > 0 having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data associated with the initial and boundary values.