Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems

Abstract

Rational Lax hierarchies introduced by Krichever are generalized. A systematic construction of infinite multi-Hamiltonian hierarchies and related conserved quantities is presented. The method is based on the classical R-matrix approach applied to Poisson algebras. A proof, that Poisson operators constructed near different points of Laurent expansion of Lax functions are equal, is given. All results are illustrated by several examples.

28 pages

References in corpus (4)

• Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theory
• Classical $\mathbf{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras
• From dispersionless to soliton systems via Weyl-Moyal like deformations
• Recursion Operator and Rational Lax Representation

Cited by in corpus (10)

• Classical R-matrix theory for bi-Hamiltonian field systems
• Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities
• Dispersionful analogue of the Whitham hierarchy
• Integrable discrete systems on R and related dispersionless systems
• Classical $r$-matrix like approach to Frobenius manifolds, WDVV equations and flat metrics
• Coupled Dispersionless and Generalized Heisenberg Ferromagnet Equations with Self-Consistent Sources: Geometry and Equivalence
• On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems
• Dispersionless Limits of Some Integrable Equations
• Recursion operator for a system admitting Lax representation with non-rational Lax function
• Dispersionless Limits of Integrable Generalized Heisenberg Ferromagnet Equations