Hydrodynamic Reductions of Dispersionless Harry Dym Hierarchy

Abstract

We investigate the reductions of dispersionless Harry Dym hierarchy to systems of finitely many partial differential equations. These equations must satisfy the compatibility condition and they are diagonalizable and semi-Hamiltonian. By imposing a further constraint, the compatibility is reduced to a system of algebraic equations, whose solutions are described.

15 pages

References in corpus (20)

• Integrable Hierarchies and Dispersionless Limit
• Integrable Structure of Interface Dynamics
• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Conformal maps and dispersionless integrable hierarchies
• Einstein-Weyl geometry, the dKP equation and twistor theory
• Solution of the dispersionless Hirota equations
• Hydrodynamic reductions and solutions of a universal hierarchy
• Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
• Laplacian Growth and Whitham Equations of Soliton Theory
• Classical $\mathbf{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras
• Energy-dependent potentials revisited: A universal hierarchy of hydrodynamic type
• On Associativity Equations in Dispersionless Integrable Hierarchies
• Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method
• Einstein--Weyl spaces and dispersionless Kadomtsev--Petviashvili equation from Painlevé I and II
• Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type
• On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies
• The integrable hierarchy constructed from a pair of KdV-type hierarchies and its associated $W$ algebra
• Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems
• Multi-matrix models without continuum limit
• On the Benney Hierarchy: free energy, string equation and quantization

Cited by in corpus (2)

• Classification of integrable hydrodynamic chains and generating functions of conservation laws
• Transformations of integrable hydrodynamic chains and their hydrodynamic reductions