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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
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