Publications [#362567] of Stephanos Venakides

Papers Published

1. Belov, S; Venakides, S, Perturbation of Riemann-Hilbert jump contours: smooth parametric dependence with application to semiclassical focusing NLS (August, 2011)
   (last updated on 2026/01/14)

   Abstract:
   A perturbation of a class of scalar Riemann-Hilbert problems (RHPs) with the jump contour as a finite union of oriented simple arcs in the complex plane and the jump function with a $z\log z$ type singularity on the jump contour is considered. The jump function and the jump contour are assumed to depend on a vector of external parameters $\vec\beta$. We prove that if the RHP has a solution at some value $\vec\beta_0$ then the solution of the RHP is uniquely defined in a some neighborhood of $\vec\beta_0$ and is smooth in $\vec\beta$. This result is applied to the case of semiclassical focusing NLS.