Thomas L. Szabo
Imaging Systems, Hewlett Packard, 3000 Minuteman Rd., Andover, MA 01810
Burgers' equation applies to finite-amplitude waves propagating in a medium with absorption that has a quadratic frequency dependence. Numerical solutions of a modified Burgers' equation have been obtained in the frequency domain for other types of losses; however, a complete set of time domain nonlinear equations corresponding to power law attenuation has not been available. Power law attenuation is defined by the equation, (alpha)((omega))=(alpha)[sub 0]|(omega)|[sup y], where (alpha)[sub 0] and y are arbitrary real constants, and (omega) is angular frequency. Blackstock [J. Acoust. Soc. Am. 77, 2050--2053 (1985)] has suggested that Burgers' equation could be generalized if an appropriate operator L could be found such that the equation could become p[sub z]-L*p=Bpp[sub (tau)], where p is pressure, B is a constant, (tau) is delayed time, and the subscripts denote derivative operations. The L operators have been derived based on a new causality principle and parabolic wave equations for power law loss. The resulting time domain equations extend Burgers' approach to finite amplitude propagation in media with arbitrary power law absorption.