Bäcklund transformations for new integrable hierarchies related to the polynomial Lie algebra \(\mathfrak{gl}_{\infty}^{(n)}\)

DOI10.1016/j.geomphys.2006.03.011zbMath1160.37027OpenAlexW1976628939WikidataQ115353440 ScholiaQ115353440MaRDI QIDQ864245

Johan W. van de Leur

Publication date: 13 February 2007

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2006.03.011

zbMATH Keywords

Lax equationBäcklund-Darboux transformationintegrable hierarchyZakharov-Shabat equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (5)

Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy ⋮ Free-field realizations of the W_{𝒜 n , N} -algebra ⋮ Constructing nonlinear discrete integrable Hamiltonian couplings ⋮ The Frobenius-Virasoro algebra and Euler equations ⋮ The Frobenius-Virasoro algebra and Euler equations. II: Multi-component cases

Cites Work

• Unnamed Item
• A vector potential KdV equation and vector Ito equation: Soliton solutions, bilinear Bäcklund transformations and Lax pairs.
• Dressing method and the coupled KP hierarchy
• Geometric Bäcklund-Darboux transformations for the KP hierarchy
• New integrable hierarchies from vertex operator representations of polynomial Lie algebras
• The Painleve property transformed
• The n-component KP hierarchy and representation theory

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