Math @ Duke

Publications [#244168] of Stephanos Venakides
Papers Published
 Tovbis, A; Venakides, S, Determinant form of the complex phase function of the steepest descent analysis of RiemannHilbert problems and its application to the focusing nonlinear schrödinger equation,
International Mathematics Research Notices, vol. 2009 no. 11
(February, 2009),
pp. 20562080, Oxford University Press (OUP), ISSN 10737928 [doi]
(last updated on 2019/04/24)
Abstract: We derive a determinant formula for the gfunction that plays a key role in the steepest descent asymptotic analysis of the solution of 2 × 2 matrix RiemannHilbert 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.


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