THE GENERALIZED KORTEWEG–DE VRIES EQUATION ON THE HALF LINE

Abstract. The initial-boundary value problem for the generalized Korteweg-de Vries equation on a half-line is studied by adapting the initial value techniques developed by Kenig, Ponce and Vega and Bourgain to the initial-boundary setting. The approach consists of replacing the initial-boundary problem by a forced initial value problem. The forcing is selected to satisfy the boundary condition by inverting a Riemann-Liouville fractional integral. This paper introduces a method to solve initial-boundary value problems for nonlinear dispersive partial differential equations by recasting these problems as initial value problems with an appropriate forcing term. This reformulation transports the robust theory of initial value problems to the initial-boundary value setting. The

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