Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces

DOI10.1063/1.525943zbMath0523.58023OpenAlexW1985549484MaRDI QIDQ3673730

Ernest G. Kalnins, C. P. Bover, Pavel Winternitz

Publication date: 1983

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

Full work available at URL: https://hdl.handle.net/10289/1225

zbMATH Keywords

hyperboloidsingular potentialLaplace-Beltrami equationCartan subgroup

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Hamilton's principle (70H25)

Related Items (12)

Klein-Gordon equation with superintegrable systems: Kepler-Coulomb, harmonic oscillator, and hyperboloid ⋮ Integrable systems based on SU(p,q) homogeneous manifolds ⋮ Abelian integrals and the reduction method for an integrable Hamiltonian system ⋮ Classical and quantum integrable systems in \(\widetilde{\mathfrak gl}(2)^{+*}\) and separation of variables ⋮ Mutually inverse series relating Ferrers and associated Legendre functions and generating functions pertaining to them ⋮ Non-Hermitian superintegrable systems ⋮ Superintegrability on the two-dimensional hyperboloid ⋮ Equations of motion and wave functions in spherical coordinates for an integrable Hamiltonian system ⋮ Pseudo-orthogonal groups and integrable dynamical systems in two dimensions ⋮ Superintegrability in three-dimensional Euclidean space ⋮ Superintegrability on the two-dimensional hyperboloid. II ⋮ Maximal abelian subalgebras of pseudounitary Lie algebras

Cites Work

• Systems of ordinary differential equations with nonlinear superposition principles
• Nonlinear action of Lie groups and superposition principles for nonlinear differential equations
• A nonlinear superposition principle admitted by coupled Riccati equations of the projective type
• Reduction of symplectic manifolds with symmetry
• Separable coordinates for four-dimensional Riemannian spaces
• Normal forms of elements of classical real and complex Lie and Jordan algebras
• Killing Tensors and Nonorthogonal Variable Separation for Hamilton–Jacobi Equations
• Subgroups of Lie groups and separation of variables
• The maximal solvable subgroups of the SU(p,q) groups and all subgroups of SU(2,1)
• Invariants of real low dimension Lie algebras
• Symmetry and separation of variables for the Hamilton–Jacobi equation W2t−W2x −W2y =0
• Hamiltonian group actions and dynamical systems of calogero type
• Maximal abelian subalgebras of real and complex symplectic Lie algebras

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