Robin boundary condition and shock problem for the focusing nonlinear Schrödinger equation

We consider the initial boundary value (IBV) problem for the focusing nonlinear Schrödinger equation in the quarter plane $x>0,t>0$ in the case of periodic initial data (at $t=0$) and a Robin boundary condition at $x=0$. Our approach is based on the simultaneous spectral analysis of the Lax pair equations combined with symmetry considerations for the corresponding Riemann-Hilbert problems. A connection between the original IBV problem and an associated initial value (IV) problem is established.

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