GranMa 2011
Oct 3 - 6, 2011
Institut Henri Poincaré, Paris
Stephanos Venakides, Duke University:
The steepest-descent method for Riemmann-Hilbert problems: the case of the focusing nonlinear Schroedinger equation
We apply the steepest-decent method to the Riemann-Hilbert problem that describes the inverse scattering corresponding to the focusing nonlinear Schroedinger equation (NLS). Steepest descent applies in an asymptotic limit, in which NLS displays its dispersive character particularly well. The initial profile breaks into fully nonlinear modulated oscillations in the small space and time scales. The oscillations are often multi-phase. The branch-points on the contour of the model Riemann-Hilbert problem are off the real axis.
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