  We study, both analytically and by numerical modeling the equilibrium
probability density function for an non-linear L\'{e}vy oscillator with the
L\'{e}vy index \alpha, 1 \leq \alpha \leq 2, and the potential energy x^4. In
particular, we show that the equilibrium PDF is bimodal and has power law
asymptotics with the exponent -(\alpha +3).
