1211.7111 (Sergey Belov et al.)

Smooth parametric dependence of asymptotics of the semiclassical
focusing NLS    [PDF]

Sergey Belov, Stephanos Venakides

We consider the one dimensional focusing (cubic) Nonlinear Schr\"odinger equation (NLS) in the semiclassical limit with a one parameter family of exponentially decaying in absolute value initial conditions. We prove smooth parametric dependence of the asymptotic solution on the parameter utilizing the Riemann-Hilbert approach. Numerical computations supporting our estimates of important quantities are presented.

View original: http://arxiv.org/abs/1211.7111