A model equation that describes the nonlinear propagation of directive ultrasound beams in an inhomogeneous medium is derived based on weak inhomogeneity and nonlinearity. Sound absorption and velocity dispersion are excluded in the analysis for simplicity. The resultant beam equation that is valid in the parabolic approximation is the same form as a general equation when the nonlinearity is negligibly small. The pressure amplitude changes of the first three harmonics are numerically predicted for a 40-kHz finite-amplitude airborne CW propagating through the inhomogeneous region, where the speed of sound is different from the host medium and whose geometrical size is much larger than the wavelength. It has been shown that the second and more higher harmonic amplitudes are less sensitive to the inhomogeneity compared with the hypothetically emitted linear beams with the same frequencies as the harmonics.
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