O. V. Rudenko
Dept. of Acoust. Phys., Faculty, Moscow State Univ., Moscow 119899, Russia
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.]