## 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 language | English |
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Pages (from-to) | 393-399 |

Number of pages | 7 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 222 |

Issue number | 6 |

DOIs | |

Publication status | Published - 18 Nov 1996 |

Externally published | Yes |