Deformations of dispersionless KdV hierarchies

Abstract

The obstructions to the existence of a hierarchy of hydrodynamic conservation laws are studied for a multicomponent dispersionless KdV system. It is shown that if an underlying algebra is Jordan, then the lowest obstruction vanishes and that all higher obstructions automatically vanish. Deformations of these multicomponent dispersionless KdV-type equations are also studied. No new obstructions appear, and hence the existence of a fully deformed hierarchy depends on the existence of a single purely hydrodynamic conservation law.

12 papges

References in corpus (2)

• Deformations of bihamiltonian structures of hydrodynamic type
• Darboux first integral conditions and integrability of the 3D Lotka-Volterra system

Cited by in corpus (4)

• Darboux first integral conditions and integrability of the 3D Lotka-Volterra system
• Deformations of the Monge/Riemann hierarchy and approximately integrable systems
• Extension of Moyal-deformed hierarchies of soliton equations
• Frobenius manifolds and Frobenius algebra-valued integrable systems