Vessiot structure for manifolds of $(p,q)$-hyperbolic type: Darboux integrability and symmetry

DOI10.1090/S0002-9947-00-02670-2zbMath0984.58003OpenAlexW1537779810MaRDI QIDQ2701677

Peter J. Vassiliou

Publication date: 19 February 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02670-2

zbMATH Keywords

hyperbolic semilinear equationsDarboux-integrability

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Moduli problems for differential geometric structures (58D27) Invariance and symmetry properties for PDEs on manifolds (58J70) Hyperbolic equations on manifolds (58J45)

Related Items (8)

A solvable string on a Lorentzian surface ⋮ On the non-integrability of a generalized Darboux Halphen system ⋮ Darboux integrability for diagonal systems of hydrodynamic type ⋮ Hyperbolic reduction ⋮ Method for Solving the Multidimensional n-Wave Resonant Equations and Geometry of Generalized Darboux-Manakov-Zakharov Systems ⋮ Superposition formulas for exterior differential systems ⋮ Isometric embedding and Darboux integrability ⋮ An integrable system of partial differential equations on the special linear group

Cites Work

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• Characteristics and the geometry of hyperbolic equations in the plane
• Internal, external, and generalized symmetries
• Rigidity of integral curves of rank 2 distributions
• The variational bicomplex for hyperbolic second-order scalar partial differential equations in the plane
• Generalized Laplace invariants and the method of Darboux
• Hyperbolic exterior differential systems and their conservation laws. II
• Sur les faisceaux de transformations infinitesimales associes aux équations aux dérivées partielles du second ordre \(F(x,y,z,p,q,r,s,t)=0\)
• On local equivalence for vector field systems
• Classification of Second-Order Ordinary Differential Equations Admitting Lie Groups of Fibre-Preserving Point Symmetries
• On some geometry associated with a generalised Toda lattice
• The symmetries of solitons
• A differential geometric generalization of characteristics

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