Nonlinear acoustic waves in channels with variable cross sections

The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted symmetry group is extended and the invariant solutions corresponding to these profiles are obtained. Approximate analytic solutions to the generalized Webster equation are derived for channels with smoothly varying cross sections and arbitrary initial conditions.Comment: Revtex4, 10 pages, 2 figure. This is an enlarged contribution to Acoustical Physics, 2012, v.58, No.3, p.269-276 with modest stylistic corrections introduced mainly in the Introduction and References. Several typos were also correcte

Shape of the inflaton potential and the efficiency of the universe heating

It is shown that the efficiency of the universe heating by an inflaton field depends not only on the possible presence of parametric resonance in the production of scalar particles but also strongly depends on the character of the inflaton approach to its mechanical equilibrium point. In particular, when the inflaton oscillations deviate from pure harmonic ones toward a succession of step functions, the production probability rises by several orders of magnitude. This in turn leads to a much higher temperature of the universe after the inflaton decay, in comparison to the harmonic case. An example of the inflaton potential is presented which creates a proper modification of the evolution of the inflaton toward equilibrium and does not destroy the nice features of inflation.Comment: 14 pages, 12 figures; final version published in EPJ