Integrability properties of some equations obtained by symmetry reductions

DOI10.1080/14029251.2015.1023582zbMath1420.35021OpenAlexW1984666815MaRDI QIDQ5230985

H. Baran, I. S. Krasil'shchik, Oleg I. Morozov, Petr Vojčák

Publication date: 29 August 2019

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

Full work available at URL: https://doi.org/10.1080/14029251.2015.1023582

zbMATH Keywords

solutionspartial differential equationssymmetry reductionsGibbons-Tsarev equationLax-integrable equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (10)

Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields ⋮ Nonlocal symmetries of integrable linearly degenerate equations: a comparative study ⋮ Infinitely many nonlocal conservation laws for the \textit{ABC} equation with \(A+B+C\neq 0\) ⋮ On the linearization covering technique and its application to integrable nonlinear differential systems ⋮ Nonlinear nonisospectral differential coverings for the hyper-CR equation of Einstein-Weyl structures and the Gibbons-Tsarev equation ⋮ Reductions of the universal hierarchy and rdDym equations and their symmetry properties ⋮ Coverings over Lax integrable equations and their nonlocal symmetries ⋮ Lie symmetry reductions and group invariant solutions of \((2+1)\)-dimensional modified Veronese web equation ⋮ 2D reductions of the equation u _yy = u _tx + u _yu _xx − u _xu _xy and their nonlocal symmetries ⋮ Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation

Uses Software

• Jets

Cites Work

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• A natural geometric construction underlying a class of Lax pairs
• Non-homogeneous systems of hydrodynamic type possessing Lax representations
• A class of Einstein-Weyl spaces associated to an integrable system of hydrodynamic type
• Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations
• Geometry of jet spaces and integrable systems
• Cartan's structure of symmetry pseudo-group and coverings for the \(r\)-th modified dispersionless Kadomtsev-Petviashvili equation
• Reductions of the Benney equations.
• A recursion operator for the universal hierarchy equation via Cartan's method of equivalence
• Hydrodynamic reductions and solutions of a universal hierarchy
• The Kupershmidt hydrodynamic chains and lattices
• Integrable hydrodynamic chains
• Symmetry reductions and exact solutions of Lax integrable 3-dimensional systems
• Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type

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