The focusing nonlinear Schrödinger equation on the quarter plane with time-periodic boundary condition: a Riemann–Hilbert approach
AB De Monvel, V Kotlyarov - Journal of the Institute of Mathematics of …, 2007 - cambridge.org
Journal of the Institute of Mathematics of Jussieu, 2007•cambridge.org
We consider the focusing nonlinear Schrödinger equation on the quarter plane. Initial data
vanish at infinity while boundary data are time-periodic. The main goal of this paper is to
introduce a Riemann–Hilbert problem whose solution gives the solution of our initial–
boundary-value problem. This is a preliminary step to obtain uniform long-time asymptotics
for the solution of this equation using both the stationary phase and the Deift–Zhou methods.
vanish at infinity while boundary data are time-periodic. The main goal of this paper is to
introduce a Riemann–Hilbert problem whose solution gives the solution of our initial–
boundary-value problem. This is a preliminary step to obtain uniform long-time asymptotics
for the solution of this equation using both the stationary phase and the Deift–Zhou methods.
We consider the focusing nonlinear Schrödinger equation on the quarter plane. Initial data vanish at infinity while boundary data are time-periodic. The main goal of this paper is to introduce a Riemann–Hilbert problem whose solution gives the solution of our initial–boundary-value problem. This is a preliminary step to obtain uniform long-time asymptotics for the solution of this equation using both the stationary phase and the Deift–Zhou methods.
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