On the geometry of Darboux transformations for the KP hierarchy and its connection with the discrete KP hierarchy

DOI10.1007/s002200050166zbMath0891.35140OpenAlexW2085795822MaRDI QIDQ1379538

Franco Magri, Jorge P. Zubelli, Marco Pedroni

Publication date: 25 February 1998

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

Full work available at URL: https://doi.org/10.1007/s002200050166

zbMATH Keywords

Darboux transformation KP hierarchy modified KP hierarchy Darboux covering Darboux-KP hierarchy geometric point of view

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) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

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Miura and Darboux transformations in the SUSY KP hierarchies ⋮ A new discrete integrable system derived from a generalized Ablowitz-Ladik hierarchy and its Darboux transformation ⋮ A lattice hierarchy and its continuous limits ⋮ A lattice hierarchy with a free function and its reductions to the Ablowitz-Ladik and Volterra hierarchies ⋮ Super KP equations and Darboux transformations: Another perspective on the Jacobian super KP hierarchy ⋮ A generalized Ablowitz–Ladik hierarchy, multi-Hamiltonian structure and Darboux transformation ⋮ Bi-Hamiltonian aspects of a matrix Harry Dym hierarchy ⋮ \(q\)-analogue of modified KP hierarchy and its quasi-classical limit ⋮ An elementary approach to the polynomial \(\tau\)-functions of the KP-hierarchy

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