### ASA 127th Meeting M.I.T. 1994 June 6-10

## 2pPA9. Self-focusing of sound beams in cubic nonlinear media.

**O. V. Rudenko
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*Dept. of Acoust. Phys., Faculty, Moscow State Univ., Moscow 119899,
Russia
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In usual dispersive quadratic nonlinear media, self-focusing (SF) does not
exist. In recent years, thermal SF of quasimonochromatic waves in highly
viscous liquids like glycerin, and thermal SF of sawtoothlike waves in inviscid
fluids, were observed experimentally. However, both phenomena are very inert
(characteristic stabilization time at least of order 10 s). A general question
in nonlinear wave theory is whether inertialess SF in cubic nonlinear media
without dispersion can exist (e.g., for shear waves). An acoustic beam in a
cubic medium can be described by a modified KZK-type equation. It is common
practice to seek a solution (following the approach in nonlinear optics) in the
form of a harmonic wave with slowly varying amplitude A. A nonlinear
Schrodinger equation can be obtained for A which describes the increase in A
due to plane front instability. However, A decreases due to nonlinear
absorption. To investigate the real behavior of the wave, a more appropriate
analytical approach, together with computer methods, were used. It was shown
that SF has remarkable features. One can observe a marked decrease of the
beamwidth. The increase in A, however, cannot be considerable. [This work was
partially supported by NATO.]