Zero curvature representation, bi-Hamiltonian structure, and an integrable hierarchy for the Zakharov-Ito system

DOI10.1063/1.4922361zbMath1318.37012OpenAlexW1923663980MaRDI QIDQ5264392

Mathew Baxter, S. Roy Choudhury, Robert A. van Gorder

Publication date: 27 July 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4922361

zbMATH Keywords

bi-Hamiltonian structureintegrable hierarchyzero curvature representationZakharov-Ito systemLenard recursion sequence

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (1)

A soliton hierarchy associated with a spectral problem of 2nd degree in a spectral parameter and its bi-Hamiltonian structure

Cites Work

• Unnamed Item
• New examples of the auto-Bäcklund transformations and nonlinear superposition formulas for vector evolution systems
• Commutator representation of isospectral equations
• Two-component integrable systems modelling shallow water waves: the constant vorticity case
• Coupled KdV equations with multi-Hamiltonian structures
• A general approach for getting the commutator representations of the hierarchies of nonlinear evolution equations
• A new hierarchy of integrable systems and its Hamiltonian structure
• On Liouville integrability of zero-curvature equations and the Yang hierarchy
• A supertrace identity and its applications to superintegrable systems
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• The algebraic structures of isospectral Lax operators and applications to integrable equations
• Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations
• Systematic method of generating new integrable systems via inverse Miura maps
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
• Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I

This page was built for publication: Zero curvature representation, bi-Hamiltonian structure, and an integrable hierarchy for the Zakharov-Ito system