Flat bidifferential ideals and semihamiltonian PDEs

Abstract

In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law. The density and the current of this conservation law satisfy a second order system of PDEs which has a natural interpretation in the theory of flat bifferential ideals. The class of systems we consider contains important well-known examples of semihamiltonian systems. Other examples, like genus 1 Whitham modulation equations for KdV, are related to this class by a reciprocal trasformation.

18 pages. v5: formula (36) corrected; minor changes

References in corpus (3)

• Integrable hydrodynamic chains
• Separation of variables for bi-Hamiltonian systems
• A cohomological construction of integrable hierarchies of hydrodynamic type

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• Bidifferential graded algebras and integrable systems
• Integrable systems, Nijenhuis geometry and Lauricella bi-flat structures
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