Unified approach to KdV modulations

El, Gennady, Krylov, Alexander L. and Venakides, Stephanos (2001) Unified approach to KdV modulations. Communications on Pure and Applied Mathematics, 54 (10). pp. 1243-1270. ISSN 0010-3640

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Official URL: https://doi.org/10.1002/cpa.10002

Abstract

We develop a unified approach to integrating the Whitham modulation equations. Our approach is based on the formulation of the initial-value problem for the zero-dispersion KdV as the steepest descent for the scalar Riemann-Hilbert problem [6] and on the method of generating differentials for the KdV-Whitham hierarchy [9]. By assuming the hyperbolicity of the zero-dispersion limit for the KdV with general initial data, we bypass the inverse scattering transform and produce the symmetric system of algebraic equations describing motion of the modulation parameters plus the system of inequalities determining the number the oscillating phases at any fixed point on the (x, t)-plane. The resulting system effectively solves the zero-dispersion KdV with an arbitrary initial datum.

Item Type: Article
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 16 Apr 2020 14:27
Last Modified: 16 Apr 2020 14:30
URI: http://nrl.northumbria.ac.uk/id/eprint/42807

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