Perturbation of Riemann-Hilbert jump contours: smooth parametric dependence with application to semiclassical focusing NLS
Publication
, Journal Article
Belov, S; Venakides, S
August 25, 2011
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.
Duke Scholars
Publication Date
August 25, 2011
Citation
APA
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ICMJE
MLA
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Belov, S., & Venakides, S. (2011). Perturbation of Riemann-Hilbert jump contours: smooth parametric
dependence with application to semiclassical focusing NLS.
Belov, Sergey, and Stephanos Venakides. “Perturbation of Riemann-Hilbert jump contours: smooth parametric
dependence with application to semiclassical focusing NLS,” August 25, 2011.
Belov S, Venakides S. Perturbation of Riemann-Hilbert jump contours: smooth parametric
dependence with application to semiclassical focusing NLS. 2011 Aug 25;
Belov, Sergey, and Stephanos Venakides. Perturbation of Riemann-Hilbert jump contours: smooth parametric
dependence with application to semiclassical focusing NLS. Aug. 2011.
Belov S, Venakides S. Perturbation of Riemann-Hilbert jump contours: smooth parametric
dependence with application to semiclassical focusing NLS. 2011 Aug 25;
Publication Date
August 25, 2011