Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#244168] of Stephanos Venakides

Papers Published

  1. Tovbis, A; Venakides, S, Determinant form of the complex phase function of the steepest descent analysis of Riemann-Hilbert problems and its application to the focusing nonlinear schrödinger equation, International Mathematics Research Notices, vol. 2009 no. 11 (2009), pp. 2056-2080, ISSN 1073-7928 [doi]
    (last updated on 2017/12/17)

    We derive a determinant formula for the g-function that plays a key role in the steepest descent asymptotic analysis of the solution of 2 × 2 matrix Riemann-Hilbert problems (RHPs) and is closely related to a hyperelliptic Riemann surface. We formulate a system of transcendental equations in determinant form (modulation equations), that govern the dependence of the branchpoints αj of the Riemann surface on a set of external parameters. We prove that, subject to the modulation equations, ∂g/∂αj is identically zero for all the branchpoints. Modulation equations are also obtained in the form of ordinary differential equations with respect to external parameters; some applications of these equations to the semiclassical limit of the focusing nonlinear Schrödinger equation (NLS) are discussed. © The Author 2009.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320