Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy

2006/12/01 by Laura Fontanelli, Fontanelli, Laura, Paolo Lorenzoni +5
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0612002

Revised version, 22 pages; a section on reciprocal transformations added. To appear in J. Math. Phys.

openalex publication_date 2006/12/01 · arxiv created 2008/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Harry Dym hierarchy of nonlinear evolution equations from the bi-Hamiltonian view point. This is done by using the concept of an S-hierarchy. It allows us to define a matrix Harry Dym hierarchy of commuting Hamiltonian flows in two fields that projects onto the scalar Harry Dym hierarchy. We also show that the conserved densities of the matrix Harry Dym equation can be found by means of a Riccati-type equation.

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