Classification of integrable \((2+1)\)-dimensional quasilinear hierarchies

DOI10.1007/s11232-005-0117-7zbMath1178.37072OpenAlexW1977071690MaRDI QIDQ843879

Evgeny V. Ferapontov, Karima R. Khusnutdinova, Maxim P. Pavlov

Publication date: 17 January 2010

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://figshare.com/articles/preprint/Classification_of_integrable_2_1_-dimensional_quasilinear_hierarchies/9378983

zbMATH Keywords

hydrodynamic reductionspseudopotentials

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Solutions to PDEs in closed form (35C05)

Related Items (12)

Multidimensional quasilinear first-order equations and multivalued solutions of the elliptic and hyperbolic equations ⋮ Integrability of the egorov systems of hydrodynamic type ⋮ On a class of three-dimensional integrable Lagrangians ⋮ Multidimensional nonlinear wave equations with multivalued solutions ⋮ Dispersionless Hirota equations and the genus 3 hyperelliptic divisor ⋮ A classification algorithm for integrable two-dimensional lattices via Lie-Rinehart algebras ⋮ Algebraic properties of quasilinear two-dimensional lattices connected with integrability ⋮ Classification of a subclass of quasilinear two-dimensional lattices by means of characteristic algebras ⋮ Model equation of the theory of solitons ⋮ Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor ⋮ Lower-dimensional reductions of GL(M,C) self-dual Yang Mills equation: Solutions with break of wave profiles ⋮ Integrability conditions for two-dimensional Toda-like equations

Cites Work

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• Egorov hydrodynamic chains, the Chazy equation, and the group \(SL(2,\mathbb C)\).
• On the integrability of \((2+1)\)-dimensional quasilinear systems
• Reductions of the Benney equations.
• Integrable structure of the Dirichlet boundary problem in multiply-connected domains
• Killing vectors in self-dual, Euclidean Einstein spaces
• Solution of the dispersionless Hirota equations
• Reductions and hodograph solutions of the dispersionless KP hierarchy
• A uniqueness criterion for solutions of the Robin problem for a system in elasticity theory in exterior domains

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