Math @ Duke

Publications [#244155] of Stephanos Venakides
Papers Published
 El, GA; Krylov, AL; Venakides, S, Unified approach to KdV modulations,
Communications on Pure and Applied Mathematics, vol. 54 no. 10
(October, 2001),
pp. 12431270, WILEY [doi]
(last updated on 2019/04/19)
Abstract: We develop a unified approach to integrating the Whitham modulation equations. Our approach is based on the formulation of the initialvalue problem for the zerodispersion KdV as the steepest descent for the scalar RiemannHilbert problem [6] and on the method of generating differentials for the KdVWhitham hierarchy [9]. By assuming the hyperbolicity of the zerodispersion 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 zerodispersion KdV with an arbitrary initial datum. © 2001 John Wiley & Sons, Inc.


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