Abstract
The main problem addressed in this paper is to study the local existence in time of solutions to the non-homogeneous Neumann initial boundary value problem for the Benjamin–Ono equation on a half-line. In this result, we observe the influence of the boundary data on the behavior of solutions. In order to obtain the characterization of the solution it is essential to use the theory concerning the Riemann–Hilbert problem. We prove local existence in time of the solutions.
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