Nonlinear action of Lie groups and superposition principles for nonlinear differential equations

DOI10.1016/0378-4371(82)90268-0zbMath0515.58019OpenAlexW2077095606WikidataQ115363223 ScholiaQ115363223MaRDI QIDQ1051958

Pavel Winternitz

Publication date: 1982

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-4371(82)90268-0

zbMATH Keywords

nonlinear differential equationsBäcklund transformationsseparation of variablesmatrix Riccati equationsuperposition principlescompletely integrable Hamiltonian systemsnonlinear actionprimitive filtered Lie algebras

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)

Related Items (7)

Lie algebras with finite-dimensional polynomial centralizer ⋮ Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles ⋮ Normal forms of elements of classical real and complex Lie and Jordan algebras ⋮ Coupled systems of nonlinear wave equations and finite-dimensional Lie algebras. I ⋮ Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces ⋮ A REDUCE program for determining point and contact Lie symmetries of differential equations ⋮ Riccati equations and Lie series

Cites Work

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• Classification of the Finite Nonlinear Primitive Lie Algebras
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• An algebraic model of transitive differential geometry

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