Nonlinear acoustic waves in channels with variable cross sections |
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| Authors: | V F Kovalev O V Rudenko |
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| Institution: | 1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia
2. Faculty of Physics, Moscow State University, Moscow, 119991, Russia
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| Abstract: | The point symmetry group is studied for the generalized Webster-type equation describing nonlinear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the allowed 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. |
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