Integration of nonlinear dynamical systems associated with finite-dimensional Lie algebras

1992 ◽  
pp. 125-166
Author(s):  
A. N. Leznov ◽  
M. V. Saveliev
Keyword(s):  
Dynamical Systems ◽  
Lie Algebras ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Finite Dimensional ◽  
Finite Dimensional Lie Algebras

scholarly journals Interplay of symmetries and other integrability quantifiers in finite-dimensional integrable nonlinear dynamical systems

2016 ◽  
Vol 472 (2190) ◽  
pp. 20150847
Author(s):  
R. Mohanasubha ◽  
V. K. Chandrasekar ◽  
M. Senthilvelan ◽  
M. Lakshmanan
Keyword(s):  
Dynamical Systems ◽  
Integrable Systems ◽  
Analytical Methods ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Ordinary Differential Equations ◽  
Lie Point Symmetries ◽  
Darboux Polynomials ◽  
Nonlinear Dynamical ◽  
Finite Dimensional ◽  
Integrating Factors

In this work, we establish a connection between the extended Prelle–Singer procedure and other widely used analytical methods to identify integrable systems in the case of n th-order nonlinear ordinary differential equations (ODEs). By synthesizing these methods, we bring out the interlink between Lie point symmetries, contact symmetries, λ-symmetries, adjoint symmetries, null forms, Darboux polynomials, integrating factors, the Jacobi last multiplier and generalized λ-symmetries corresponding to the n th-order ODEs. We also prove these interlinks with suitable examples. By exploiting these interconnections, the characteristic quantities associated with different methods can be deduced without solving the associated determining equations.

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