Well-posedness of the initial-boundary value problem for the Hirota equation on the half line

Abstract

In this paper we study the regularity properties of Hirota equation on the right half line with data of low regularity. In particular, using an explicit solution formula of the initial and boundary value problem and the restricted norm method, we prove the local existence, uniqueness, and continuous dependence on initial data in Xs,b spaces. Moreover, we obtain the global existence and that the nonlinearity of Hirota equation on the half line is smoother than the initial data.