Projection of the Khokhlov-Zabolotskaya Equation on the Axis of Wave Beam As a Model of Nonlinear Diffraction

An equation is obtained that describes the nonlinear diffraction of a focused wave in a half-space starting from the wave source, then through the focus region up to the far zone, where the wave becomes spherically divergent. In contrast to the Khokhlov-Zabolotskaya equation (KZ), which contains two spatial variables, the calculation of the field on the beam axis is reduced to a simpler one-dimensional problem. Integral relations that are useful for numerical calculation are indicated. The profiles of a periodic wave harmonic at the input to the medium are constructed. A comparison with the results of a numerical solution of problems based on KZ is made, which revealed a good accuracy of the approximate model. The passage of a wave through the focus region, accompanied by the formation of shock fronts, diffraction phase shifts and asymmetric distortion of regions of different polarity, is traced.

Lapshin, E. A.Moscow MV Lomonosov State Univ., RUS (author)
Rudenko, OlegBlekinge Tekniska Högskola,Institutionen för maskinteknik(Swepub:bth)oru (author)
Moscow State Univ., RUSMoscow MV Lomonosov State Univ., RUS (creator_code:org_t)

In:Doklady. Mathematics: MAIK NAUKA/INTERPERIODICA/SPRINGER96:3, s. 646-6491064-56241531-8362

About the subject

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.