×

The focusing nonlinear Schrödinger equation on the quarter plane with time-periodic boundary condition: A Riemann-Hilbert approach. (English) Zbl 1180.35474

Summary: 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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
35Q15 Riemann-Hilbert problems in context of PDEs
PDF BibTeX XML Cite
Full Text: DOI