Exact steady-state solution of FKP equation in higher dimension for a class of non linear Hamiltonian dissipative dynamical systems excited by Gaussian white noise

Abstract

This paper deals with the study of nonlinear stochastic dynamical systems. We have obtained an exact steay-state probability density function for a class of multi-dimensional nonlinear Hamiltonian dissipative dynamical systems excited by Gaussian white noise. The damping can be nonlinear and parametric excitation can be taken into account. When the Hamiltonian function has a radial form, an explicit expression of the Fourier transform of the probability density function is obtained. In this case, for any finite dimension of the system, one can easily calculate any moments of random variables, by using this characteristic function.