Initial boundary value problem for the focusing NLS 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 $x\to +\infty$) and the Robin boundary condition at $x=0$. We revisit the approach based on the simultaneous spectral analysis of the Lax pair equations [Fokas, 2002; Fokas, Its, Sung, 2005] and show that the approach can be implemented without any a priori assumptions on the long-time behavior of the boundary values.

15 pages; Introduction and Concluding remarks enhanced

References in corpus (2)

• The Nonlinear Schrödinger Equation on the Interval
• Breathing patterns in nonlinear relaxation

Cited by in corpus (1)

• The Robin problem for the nonlinear Schrödinger equation on the half-line