Stochastic wave-kinetic theory in the Liouville approximation


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AIP Publishing


The behavior of scalar wave propagation in a wide class of asymptotically conservative, dispersive, weakly inhomogeneous and weakly nonstationary, anisotropic,random media is investigated on the basis of a stochastic, collisionless, Liouville_type equation governing the temporal evolution of a phase_space Wigner distribution density function. Within the framework of the first_order smoothing approximation, a general diffusion-convolution_type kinetic or transport equation is derived for the mean phase_space distribution function containing generalized (nonloral, with memory) diffusion,friction, and absorption operators in phase space. Various levels of simplification are achieved by introducing additional constraints. In the long_time, Markovian, diffusion approximation, a general set of Fokker-Planck equations is derived. Finally, special cases of these equations are examined for spatially homogeneous systems and isotropic media.



Diffusion, Anisotropy, Collision theories, Cumulative distribution functions, Density functional theory, Friction, Operator equations, Random media, Wave propagation


Besieris, I. M.; Tappert, F. D., "Stochastic wave-kinetic theory in the Liouville approximation," J. Math. Phys. 17, 734 (1976);