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

We consider the initial boundary value (IBV) problem for focusing nonlinear Schrodinger equation in quarter plane x>0, t >0 case of periodic data, u(x,0) = ? exp(?2i?x) (or asymptotically periodic, u(x, 0) =? exp(?2i?x)?0 as x??), and a Robin condition at x 0: ux(0, t)+qu(0, t) 0, q ? 0. Our approach is based on unified transform (the Fokas method) combined with symmetry considerations corresponding Riemann-Hilbert (RH) problems. present representation solution IBV terms an associated RH problem. This also allows us to determine (IV) problem, shock type, which being restricted half-line > 0 original In ? 0,...