Smooth parametric dependence of asymptotics of the semiclassical   focusing NLS
  We consider the one dimensional focusing (cubic) Nonlinear Schr\"odinger equation (NLS) in the semiclassical limit with exponentially decaying complex-valued initial data, whose phase is multiplied by a real parameter. We prove smooth dependence of the asymptotic solution on the parameter. Numerical results supporting our estimates of important quantities are presented. 
Sergey Belov and Stephanos Venakides
math.AP math-ph math.MP