A study of the propagation and interaction of two collinear finite amplitude sound beams, presented in a previous paper [Naze Tjo/tta et al., “Propagation and interaction of two collinear finite amplitude sound beams,” J. Acoust. Soc. Am. 88, 2859–2870 (1990)] is extended to include the effects of focusing. The validity of the parabolic equation when applied to strongly focused sound beams is discussed. Equations and algorithms based on a transformed parabolic equation are presented and used to compute the interaction between two collinear, focused sound beams, and between one plane wave and a focused sound beam. Numerical results are shown, with special emphasis on parametric generation and parametric reception of sound.
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tta et al. (1991) studied this question.