Group theoretical approach to superposition rules for systems of Riccati equations

DOI10.1007/BF00403243zbMath0474.34011OpenAlexW2052957771MaRDI QIDQ1159309

J. Harnad, Robert L. Anderson, Pavel Winternitz

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1007/bf00403243

zbMATH Keywords

group theoretical structureRiccati systems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34)

Related Items (20)

Superposition formulas for pseudounitary matrix Riccati equations ⋮ Complex parabolic subgroups of \(G_ 2\) and nonlinear differential equations ⋮ Nonlinear differential equations and Lie superalgebras ⋮ Multisymplectic structures and invariant tensors for Lie systems ⋮ A NEW LIE–SYSTEMS APPROACH TO SECOND-ORDER RICCATI EQUATIONS ⋮ Positive similarity solutions for a discrete velocity Boltzmann coagulation-fragmentation model ⋮ Comments on superposition rules for nonlinear coupled first-order differential equations ⋮ Superposition principles for matrix Riccati equations ⋮ A generalization of a SIS epidemic model with fluctuations ⋮ Lie–Hamilton systems on curved spaces: a geometrical approach ⋮ Infinite-dimensional homogeneous manifolds with translational symmetry and nonlinear partial differential equations ⋮ Superposition rules, Lie theorem, and partial differential equations ⋮ A Lie systems approach to the Riccati hierarchy and partial differential equations ⋮ \(k\)-symplectic Lie systems: theory and applications ⋮ Coupled systems of nonlinear wave equations and finite-dimensional Lie algebras. I ⋮ Systems of ordinary differential equations with nonlinear superposition principles ⋮ LIE–HAMILTON SYSTEMS: THEORY AND APPLICATIONS ⋮ Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras ⋮ Riccati equations and Lie series ⋮ On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems

Cites Work

• Systems of ordinary differential equations with nonlinear superposition principles
• A nonlinear superposition principle admitted by coupled Riccati equations of the projective type
• Linear and Riccati systems

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