TY - JOUR

T1 - Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem

AU - El, G. A.

PY - 1996/11/18

Y1 - 1996/11/18

N2 - 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.

AB - 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.

KW - Dispersive shocks

KW - Integrable hierarchies

KW - Whitham equations

UR - http://www.scopus.com/inward/record.url?scp=13544265603&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(96)00667-6

DO - 10.1016/S0375-9601(96)00667-6

M3 - Article

AN - SCOPUS:13544265603

SN - 0375-9601

VL - 222

SP - 393

EP - 399

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 6

ER -