摘要：In this study, we consider a Lienard II-type harmonic nonlinear oscillator equation as a nonlinear dynamical system. Firstly, we examine the first integrals in the form A ( t , x ) x ˙ + B ( t , x ) $A(t,x)\dot{x}+B(t,x)$ , the corresponding exact solutions and the integrating factors. In addition, we analyze other types of the first integrals via the λ-symmetry approach. We show that the equation can be linearized by means of a nonlocal transformation, the so-called Sundman transformation. Furthermore, using the modified Prelle-Singer approach, we point out that explicit time-independent first integrals can be identified for the Lienard II-type harmonic nonlinear oscillator equation.
关键词：dynamical systems ; first integrals ; λ -symmetries ; integrating factors ; Sundman transformation ; Prelle-Singer procedure ; Lagrangian and Hamiltonian description
