Radius of analyticity for the Camassa-Holm equation on the line

Using estimates in Sobolev spaces we prove that the solution to the Cauchy problem for the Camassa-Holm equation on the line with analytic initial data u(0)(x) and satisfying the McKean condition, that is the quantity m(0)(x) = (1 - (2)(partial derivative x))u(0)(x) does not change sign, is analytic in the spatial variable for all time. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity r(t) given by r(t) >= A(-1) (1 + C(1)Bt)(-1) exp{-C-0 parallel to u(0)parallel to(H1t)}, where A, B, C-1 and C-0 are suitable positive constants. (C) 2018 Elsevier Ltd. All rights reserved.