Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras

DOI10.1007/BF00420043zbMath0546.34008OpenAlexW2060413593MaRDI QIDQ798488

Pavel Winternitz, Steven Shnider

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1007/bf00420043

zbMATH Keywords

superposition principlesprimitive transitive filtered Lie algebras

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34)

Related Items

Lie algebras with finite-dimensional polynomial centralizer, Complex parabolic subgroups of \(G_ 2\) and nonlinear differential equations, Classification of systems of nonlinear ordinary differential equations with superposition principles, Nonlinear differential equations and Lie superalgebras, Lie-theoretical generalization and discretization of the Pinney equation, Contact Lie systems: theory and applications, Lie–Hamilton systems on curved spaces: a geometrical approach, Reduction by invariants and projection of linear representations of Lie algebras applied to the construction of nonlinear realizations, Transformation groups on real plane and their differential invariants, Dirac-Lie systems and Schwarzian equations, Bifurcation and symmetry breaking, Nonlinear superposition formulas based on imprimitive group action, Realizations of the Witt and Virasoro Algebras and Integrable Equations, Realization of semisimple lie algebras with polynomial and rational vector fields

Cites Work

• A nonlinear superposition principle admitted by coupled Riccati equations of the projective type
• Group theoretical approach to superposition rules for systems of Riccati equations
• Semi-simple real subalgebras of non-compact semi-simple real Lie algebras. IV
• The geometry and structure of isotropy irreducible homogeneous spaces
• Semi-simple real subalgebras of non-compact semi-simple real Lie algebras. III
• Superposition principles for matrix Riccati equations
• Classification of systems of nonlinear ordinary differential equations with superposition principles
• An algebraic model of transitive differential geometry