Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy

DOI10.1063/1.532540zbMath0927.37052arXivsolv-int/9609009OpenAlexW1995192590MaRDI QIDQ4701672

L. V. Bogdanov, B. G. Konopelchenko

Publication date: 21 November 1999

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

Full work available at URL: https://arxiv.org/abs/solv-int/9609009

zbMATH Keywords

dressing methodKP hierarchyintegrable hierarchysingularity manifoldCauchy-Baker-Akhiezer functionHirota identity2D Toda lattice hierarchiesCombescure symmetry groupSato method

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 (12)

Commutator identities on associative algebras, the non-abelian Hirota difference equation and its reductions ⋮ Nonlinear Beltrami equation and \(\tau \)-function for dispersionless hierarchies ⋮ The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions ⋮ Lagrangian 3-form structure for the Darboux system and the KP hierarchy ⋮ Möbius invariant integrable lattice equations associated with KP and 2DTL hierarchies ⋮ The KP hierarchy in Miwa coordinates ⋮ Generalized KP hierarchy: Möbius symmetry, symmetry constraints and Calogero-Moser system ⋮ Commutativity of the extended KP flows ⋮ Higher Hirota difference equations and their reductions ⋮ Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies ⋮ KPII: Cauchy–Jost function, Darboux transformations and totally nonnegative matrices ⋮ Cauchy-Jost function and hierarchy of integrable equations

Cites Work

• Solitons and infinite dimensional Lie algebras
• Generalized Hirota bilinear identity and integrable \(q\)-difference and lattice hierarchies
• Loop groups and equations of KdV type
• Characterization of Jacobian varieties in terms of soliton equations
• \(D\) bar dressing and Sato theory
• Birkhoff strata, Bäcklund transformations, and regularization of isospectral operators
• Dual \(\overline\partial\)-problem, \((2+1)\)-dimensional integrable nonlinear evolution equations and their reductions
• The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
• The non-local delta problem and (2+1)-dimensional soliton equations
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• Lattice and q-difference Darboux-Zakharov-Manakov systems via delta -dressing method

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