Dispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical ∂̄-dressing method

DOI10.1063/1.1481545zbMath1060.37056arXivnlin/0105071OpenAlexW2076345955MaRDI QIDQ4832693

B. G. Konopelchenko, Luis Martínez-Alonso

Publication date: 14 December 2004

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

Full work available at URL: https://arxiv.org/abs/nlin/0105071

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items (19)

On kernel formulas and dispersionless Hirota equations of the extended dispersionless BKP hierarchy ⋮ The semi-classical limit of Davey-Stewartson hierarchy ⋮ Nonlinear Beltrami equation and \(\tau \)-function for dispersionless hierarchies ⋮ Looped cotangent Virasoro algebra and nonlinear integrable systems in dimension \(2+1\) ⋮ On a class of three-dimensional integrable Lagrangians ⋮ Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type ⋮ New integrable (\(3+1\))-dimensional systems and contact geometry ⋮ Lie symmetry analysis and conservation laws for the \((2 + 1)\)-dimensional dispersionless B-type Kadomtsev-Petviashvili equation ⋮ Dispersionless integrable equations as coisotropic deformations: extensions and reductions ⋮ On the \(\overline{\delta}\)-dressing method applicable to heavenly equation ⋮ Dispersionless (3+1)-dimensional integrable hierarchies ⋮ Coisotropic deformations of associative algebras and dispersionless integrable hierarchies ⋮ SECOND-ORDER QUASILINEAR PDEs AND CONFORMAL STRUCTURES IN PROJECTIVE SPACE ⋮ Cartan's structure of symmetry pseudo-group and coverings for the \(r\)-th modified dispersionless Kadomtsev-Petviashvili equation ⋮ \(\bar \partial{}\)-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy ⋮ Kernel formula approach to the universal Whitham hierarchy ⋮ Conformal mappings and dispersionless Toda hierarchy ⋮ A note on reductions of the dispersionless Toda hierarchy ⋮ On universality of homogeneous Euler equation

Cites Work

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• Quasi-classical limit of BKP hierarchy and \(W\)-infinity symmetries
• Solitons and infinite dimensional Lie algebras
• Construction of higher-dimensional nonlinear integrable systems and of their solutions
• The dispersionless Lax equations and topological minimal models
• Conformal maps and reductions of the Benney equations
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• The quasiclassical limit of the modified KP hierarchy
• The small dispersion limit of the Korteweg-de Vries equation. III
• Quasiconformal mappings, with applications to differential equations, function theory and topology
• SDIFF(2) KP HIERARCHY
• The semiclassical limit of the defocusing NLS hierarchy
• The τ‐function of the universal whitham hierarchy, matrix models and topological field theories
• Solution of the dispersionless Hirota equations
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT

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