Initial boundary value problem for the focusing nonlinear Schrödinger equation with Robin boundary condition: half-line approach

Abstract

We consider the initial boundary value problem for the focusing nonlinear Schrödinger equation in the quarter plane x >0, t >0 in the case of decaying initial data (for t =0, as ) and the Robin boundary condition at x =0. We revisit the approach based on the simultaneous spectral analysis of the Lax pair equations and show that the method can be implemented without any a priori assumptions on the long-time behaviour of the boundary values.