Geometric structure of the classical Lagrange-d'Alembert principle and its application to integrable nonlinear dynamical systems

DOI10.3390/math5040075zbMath1430.17099OpenAlexW2774264867MaRDI QIDQ1649071

Oksana E. Hentosh, Yarema A. Prykarpatsky, Anatoliy K. Prykarpatsky

Publication date: 5 July 2018

Published in: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/math5040075

zbMATH Keywords

Hamiltonian systemLie-Poisson structureLagrange-d'Alembert principleLax integrabilityCasimir invariantsheavenly equationsLie-algebraic schemeLax-Sato equations\(\mathcal R\)-structureBuhl vector field symmetry problemloop Lie algebratorus diffeomorphisms

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Invariance and symmetry properties for PDEs on manifolds (58J70) Applications of Lie algebras and superalgebras to integrable systems (17B80)

Related Items (2)

The Lax-Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure ⋮ Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators

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