In a physical problem I need to investigate the following nonlinear differential equation

$$\ddot x+\omega^2\left (1+\frac{m^2\dot x^2}{p^2}\right)x=0,$$

where $p$ is some constant with a dimension of momentum. I will be grateful for references about such type of oscillators. So far I only found the following:

- Ronald E. Mickens, Generalized harmonic oscillators, Journal of Sound and Vibration, Volume 236, Issue 4, Pages 730-732, 28 September 2000.