In this article, a nonlinear wave equation of bounded acoustic beam in relaxating media is presented and a general solution of higher harmonics resulting from the nonlinear distortion of propagation is found by using the pertubation approach. Investigation shows that for the Gaussian ultrasonic field, the solution of higher harmonics can be given analytically, moreover their corresponding radical distributions of amplitude always maintain the Gaussian profiles. Although the dispersion may affect the amplitude of various harmonics, the variation of phase velocity of those keep the same law as the small amplitude waves of corresponding frequencies do.We also show that by means of Blackstock' operator the obtained results can be applied te the case of media with arbitrary dissipation and dispersion, including some biomedia in which the relationship between the absorption and frequency may be obtained only empirically.
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