Abstract
In this paper we study the generalized Korteweg–de Vries (KdV) equation with the nonlinear term of order three: (u3+1)x. We prove sharp local well-posedness for the initial and boundary value problem posed on the right half line. We thus close the gap in the well-posedness theory of the generalized KdV which remained open after the seminal work of Colliander and Kenig in Colliander and Kenig (2002).
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