Positive and negative integrable hierarchies, associated conservation laws and Darboux transformation

DOI10.1016/j.cam.2009.09.009zbMath1184.37055OpenAlexW2135382488MaRDI QIDQ1034665

Yuan-Qing Zhang, Xin-Yue Li, Qiu-Lan Zhao

Publication date: 6 November 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.09.009

zbMATH Keywords

conservation lawsHamiltonian structureDarboux transformationdiscrete integrable systemdiscrete zero curvature equation

Mathematics Subject Classification ID

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

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Cites Work

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• Darboux transformation of a coupled lattice soliton equation
• Positive and negative hierarchies of integrable lattice models associated with a Hamiltonian pair
• Application of Hirota's bilinear formalism to a two-dimensional lattice by Leznov
• Master Symmetries from Lax Operators for Certain Lattice Soliton Hierarchies
• Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure
• Nonlinear differential−difference equations
• A new hierarchy of integrable differential-difference equations and Darboux transformation
• R-matrix approach to lattice integrable systems
• A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations
• New Matrix Lax Representation for a Blaszak–Marciniak Four-Field Lattice Hierarchy and Its Infinitely Many Conservation Laws
• A new integrable symplectic map associated with lattice soliton equations
• A Hierarchy of Lax Integrable Lattice Equations, Liouville Integrability and a New Integrable Symplectic Map
• A trace identity and its applications to the theory of discrete integrable systems

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