  States of nonlinear quantum oscillators (f-oscillators) are considered in the
Weyl-Wigner-Moyal representation and the tomographic probability
representation, where the states are described by standard probability
distributions instead of wave functions or density matrices. The evolving
integrals of motion for classical and quantum f-oscillators are found and the
solution for the Liouville equation associated with the probability
distribution on the phase space for this oscillator is obtained along with the
solution of Moyal equation for quantum f-oscillator, which provide the
solutions for partial case of f-nonlinearity existing in Kerr media. Nonlinear
coherent states and the thermodynamics of nonlinear oscillators are studied.
