Unified approach to KdV modulations


Journal Article

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. © 2001 John Wiley & Sons, Inc.

Full Text

Duke Authors

Cited Authors

  • El, GA; Krylov, AL; Venakides, S

Published Date

  • October 1, 2001

Published In

Volume / Issue

  • 54 / 10

Start / End Page

  • 1243 - 1270

International Standard Serial Number (ISSN)

  • 0010-3640

Digital Object Identifier (DOI)

  • 10.1002/cpa.10002

Citation Source

  • Scopus