Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem

G. A. El*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

Generating functions for a complete collection of symmetries of the multiphased averaged KdV equation are constructed. The isospectral generating function has a potential form with one of the canonical basis holomorphic differentials as a potential and possesses some remarkable properties at double points of the hyperelliptic Riemann surface. A new representation for the characteristic speeds of the Whitham-KdV hierarchy is obtained. A global solution to the Whitham system is constructed in an effective form for the case of smooth decreasing initial data with a finite number of inflection points. The large time asymptotics of this solution implies the single-phase limiting behaviour of the oscillations to correlate with the asymptotic predictions of the Lax-Levermore theory.

Original languageEnglish
Pages (from-to)393-399
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume222
Issue number6
DOIs
Publication statusPublished - 18 Nov 1996
Externally publishedYes

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