Multi-dimensional transfer functions for a non-dissipative Burgers’ equation - DYBA, Roman; ŻÓŁTOGÓRSKI, Bronisław (Archives of Acoustics, 1986)
The propagation of acoustic disturbances in a continuum medium was analyzed under the assumption that the non-dissipative Burgers’ equation is a reasonable mathematical model of the phenomenon under study. Regarding the propagation as a transformation of the time dependence of the acoustic velocity in a system with an input signal and employing the Banta’s solution, the non-linear Burgers-Banta system was obtained. This system was described in the form of Volterra’s series; the kernels of the series being determined with the help of the method of harmonic excitations. The r-dimensional Volterra’s kernels given in the paper and their Fourier transforms (transfer functions) enable the parameters and probabilistic characteristics of the output signal to be determined under the condition that the input signal is known.