The solution to the \(q\)-KdV equation

DOI10.1016/S0375-9601(98)00082-6zbMath0944.37035arXivsolv-int/9712015OpenAlexW3100253315MaRDI QIDQ1966700

Pierre van Moerbeke, Mark Adler, Emil Horozov

Publication date: 8 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9712015

zbMATH Keywords

KP hierarchyGelfand-Dickey reductionKdV solution

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Lattice dynamics; integrable lattice equations (37K60)

Related Items (15)

Integrable structure of melting crystal model with two \(q\)-parameters ⋮ Lax Matrices for Yang-Baxter Maps ⋮ Two kinds of Darboux-Bäcklund transformations for the \(q\)-deformed KdV hierarchy with self-consistent sources ⋮ Rational reductions of the 2D-Toda hierarchy and mirror symmetry ⋮ Bi-Hamiltonian structures for integrable systems on regular time scales ⋮ A new extended q-deformed KP hierarchy ⋮ Hirota Formulas and Q-Hierarchies ⋮ The gauge transformation of the q-deformed modified KP hierarchy ⋮ Miura and auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies ⋮ On the \(q\)-deformed modified Korteweg-de Vries hierarchy ⋮ Strict versions of integrable hierarchies in pseudodifference operators and the related Cauchy problems ⋮ \(q\)-KP hierarchy, bispectrality and Calogero-Moser systems ⋮ Integrable discrete systems on R and related dispersionless systems ⋮ Integrable equations on time scales ⋮ Geometric Bäcklund-Darboux transformations for the KP hierarchy

Cites Work

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• Extensions and contractions of the Lie algebra of \(q\)-pseudodifferential symbols on the circle
• Loop groups and equations of KdV type
• Bispectral algebras of commuting ordinary differential operators
• Birkhoff strata, Bäcklund transformations, and regularization of isospectral operators
• General methods for constructing bispectral operators
• The bispectral property of aq-deformation of the Schur polynomials and theq-KdV hierarchy
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT

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