Abstract
The anisotropic wave collapses governed by the Zakharov equations or by the nonlinear Schrödinger equation are investigated by means of a transformation group exhibiting self-similar anisotropic solutions characterized by two contraction rates. We show the existence of two infinite sets of anisotropic self-similar collapses corresponding, respectively, to “pancake” (oblate) and “cigar” (oblong) shaped collapsing solutions. Both of these classes of anisotropic structures are furthermore shown to be bounded from below by two peculiar solutions whose validity extends from the subsonic to the supersonic regime (the so-called “trans-sonic” solutions) and from above by the standard isotropic solutions. Spatial profiles of trans-sonic anisotropic solutions are analytically derived.
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