Initial boundary value problem for the focusing NLS equation with Robin boundary condition: half-line approach

Details Initial boundary value problem for the focusing NLS equation with Robin boundary condition: half-line approach Initial boundary value problem for the focusing NLS equation with Robin boundary condition: half-line approach

2012-01-28

arxiv.org/abs/1201.5948v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages; Introduction and Concluding remarks enhanced

Scientific paper

We consider the initial boundary value problem for the focusing nonlinear Schr\"odinger 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.

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