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Symmetries; integrals of motion; integrability.

We recall six different analytical methods, namely extended Prelle–Singer procedure, Lie point symmetries, $\lambda$-symmetries, adjoint symmetries, Jacobi last multiplier and Darboux polynomial methods which are used to identify integrability quantifiers of nonlinear ordinary differential equations (ODEs).We point out how these methods are interconnected in the case of two-coupled first-order nonlinear ODEs.We demonstrate the interconnections with an example.

R MOHANASUBHA¹ V K CHANDRASEKAR² M SENTHILVELAN³

1. Department of Physics, Anna University, Chennai 600 025, India
2. Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401, India
3. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India

Published

16 September 2019