Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures

DOI10.1088/1361-6544/ad6accMaRDI QIDQ6601326

Vladimir S. Matveev, Alexei V. Bolsinov, Andrey Yu. Konyaev

Publication date: 10 September 2024

Published in: Nonlinearity (Search for Journal in Brave)

zbMATH Keywords

conservation lawintegrable systemssymmetriesquasilinear systemNijenhuis operator

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Invariant integrability criterion for equations of hydrodynamic type
• Construction of coupled Harry Dym hierarchy and its solutions from Stäckel systems
• Hamiltonian formalism of Whitham-type hierarchies and topological Landau- Ginsburg models
• Separable Hamiltonians and integrable systems of hydrodynamic type
• Bi-Hamiltonian structure of equations of associativity in 2-d topological field theory
• Invariant variational problems
• Nijenhuis geometry. II: Left-symmetric algebras and linearization problem for Nijenhuis operators
• Nijenhuis geometry
• Higher Haantjes brackets and integrability
• \(F\)-manifolds, multi-flat structures and Painlevé transcendents
• Les lois de conservation
• The existence of conservation laws. I
• From Stäckel systems to integrable hierarchies of PDE’s: Benenti class of separation relations
• Matrix Analysis
• Impossibility of the “gradient catastrophe” for slightly non-linear systems
• Existence of conservation laws and characterization of recursion operators for completely integrable systems
• Symmetry Classes of Quasilinear Systems in One Space Variable
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• ON MATRICES DEPENDING ON PARAMETERS
• Quasilinear systems of Jordan block type and the mKP hierarchy
• Nijenhuis geometry. III: \(\mathrm{gl}\)-regular Nijenhuis operators
• Applications of Nijenhuis geometry. V: Geodesic equivalence and finite-dimensional reductions of integrable quasilinear systems
• Stationary coupled KdV systems and their Stäckel representations

Related Items (2)

Hamiltonian aspects of the kinetic equation for soliton gas ⋮ Regular \(F\)-manifolds with eventual identities

This page was built for publication: Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures