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Research Article Open access CC BY 3.0

Lie Algebra Structures Associated with Zero Curvature Equations and Generalized Zero Curvature Equations

Wen-Xiu Ma

Current Journal of Applied Science and Technology · pp. 1336–1344 · Published 17 Aug 2013

10.9734/BJAST/2013/3094

Abstract

Binary operations are introduced for triples satisfying zero curvature equations and quadruples satisfying generalized zero curvature equations, and it is shown that such operations define Lie algebra structures on the corresponding spaces of triples and quadruples.

Zero curvature equation Lie algebra Symmetry

References (20)

  1. 1 Dictionary on Lie algebras and superalgebras
  2. 2 Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras [DOI]
  3. 3 On Liouville integrability of zero-curvature equations and the Yang hierarchy [DOI]
  4. 4 Semi-direct sums of Lie algebras and continuous integrable couplings [DOI]
  5. 5 The algebraic structure of zero curvature representations and application to coupled KdV systems [DOI]
  6. 6 The multi-component coupled Burgers hierarchy of soliton equations and its multi-component integrable couplings system with two arbitrary functions [DOI]
  7. 7 The algebraic structures of isospectral Lax operators and applications to integrable equations [DOI]
  8. 8 Variational identities and Hamiltonian structures [DOI]
  9. 9 Symmetries of discrete dynamical systems [DOI]
  10. 10 Lie algebraic structures of (1+1)-dimensional Lax integrable systems [DOI]
  11. 11 Integrable Couplings, Variational Identities and Hamiltonian Formulations
  12. 12 A few Lie algebras and their applications for generating integrable hierarchies of evolution types [DOI]
  13. 13 Two integrable couplings of the Tu hierarchy and their Hamiltonian structures [DOI]
  14. 14 The Liouville integrability of integrable couplings of Volterra lattice equation [DOI]
  15. 15 On the construction of recursion operator and algebra of symmetries for field and lattice systems [DOI]
  16. 16 GENERATORS OF VECTOR FIELDS AND TIME DEPENDENT SYMMETRIES OF EVOLUTION EQUATIONS
  17. 17 THE ALGEBRAIC STRUCTURE RELATED TO L-A-B TRIAD REPRESENTATIONS OF INTEGRABLE SYSTEMS [DOI]
  18. 18 THE LIE ALGEBRA STRUCTURES OF TIME DEPENDENT SYMMETRIES OF EVOLUTION EQUATIONS
  19. 19 THE NEGATIVE AND POSITIVE INTEGRABLE COUPLING HIERARCHIES DERIVED FROM A FOUR BY FOUR MATRIX SPECTRAL PROBLEM [DOI]
  20. 20 On construction of recursion operators from Lax representation

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