Abstract
Integral representation (IR), or the so-called ·wiener-Hermite expansion, is proposed as a new method of solving a class of nonlinear stochastic differential equations (NLSDE's) that appear in the theory of Brownian motion of anharmonic oscillators, semi-classical treatment of laser oscillation or in the Kraichnan-Wyld formulation of turbulence. The basic procedure of application of IR is established and simple NLSDE's are analyzed. Results for power spectral density agree well with numerical experiment data even in strongly nonlinear cases. It is also shown that IR is a completed form of renormalized perturbation expansion, and provides a systematic way to improve various approximation schemes such as fourth cumulant discard approximation or equivalent linearization procedure.
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