Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies

DOI10.1063/1.532531zbMath0927.37053arXivsolv-int/9705009OpenAlexW3106201054MaRDI QIDQ4701673

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/9705009

zbMATH Keywords

dressing methodKP hierarchyintegrable hierarchiesintegrable equationssingularity manifoldCauchy-Baker-Akhiezer function2D Toda lattice hierarchiesCombescure symmetry groupCombescure symmetry transformationSato 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 (24)

The AKNS Hierarchy Revisited: A Vertex Operator Approach and its Lie-Algebraic Structure ⋮ Commutator identities on associative algebras, the non-abelian Hirota difference equation and its reductions ⋮ Functional Representation of the AblowitzLadik Hierarchy. II ⋮ The B-quadrilateral lattice, its transformations and the algebro-geometric construction ⋮ From nonassociativity to solutions of the KP hierarchy ⋮ Integrability and geometry of the Wynn recurrence ⋮ The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions ⋮ Hermite-Padé approximation and integrability ⋮ The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system ⋮ Möbius invariant integrable lattice equations associated with KP and 2DTL hierarchies ⋮ Generating quadrilateral and circular lattices in KP theory ⋮ Quadrilateral lattices and eigenfunction potentials for \(N\)-component KP hierarchies ⋮ Burgers and Kadomtsev-Petviashvili hierarchies: a functional representation approach ⋮ Elliptic (N, N′)-soliton solutions of the lattice Kadomtsev-Petviashvili equation ⋮ Transformations of quadrilateral lattices ⋮ The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction ⋮ Generalized KP hierarchy: Möbius symmetry, symmetry constraints and Calogero-Moser system ⋮ Higher Hirota difference equations and their reductions ⋮ Three types generalized \(Z_n\)-Heisenberg ferromagnet models ⋮ Dispersionful analog of the Whitham hierarchy ⋮ Nets, lattices and multicomponent KP hierarchies ⋮ The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice ⋮ Explicit solutions of integrable lattices ⋮ 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
• Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation
• Explicit solutions to two-dimensionalized Volterra equations
• To a transformation theory of two-dimensional integrable systems
• GEOMETRY OF UNIVERSAL GRASSMANN MANIFOLD FROM ALGEBRAIC POINT OF VIEW
• SOLITON EIGENFUNCTION EQUATIONS: THE IST INTEGRABILITY AND SOME PROPERTIES
• On the one- and two-dimensional Toda lattices and the Painlevé property
• The non-local delta problem and (2+1)-dimensional soliton equations
• Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy
• Generalized integrable hierarchies and Combescure symmetry transformations
• The direct linearisation approach to hierarchies of integrable PDEs in 2 + 1 dimensions: I. Lattice equations and the differential-difference hierarchies

This page was built for publication: Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies