Yu. I. Skrynnikov
N. N. Andreev Acoust. Inst., Russian Acad. of Sci., Shvernik str. 4, 117036, Moscow, Russia
For nonlinear sound waves in media containing compact oscillators (e.g., liquid with gas bubbles or rubberlike materials with metallic small balls) an evolution equation was obtained taking into account a viscouslike term. With the help of the technique of multiple scales for singular perturbations its solution in the form of the shock wave was found. In contrast to the well-known solution of Burgers equation the front of the obtained shock wave has an unusual form with a horizontal plateau. Owing to this fact the wave energy dissipation may be easily demonstrated to be weak. Actually, the wave energy E release rate due to viscosity is proportional to dE/dt(proportional to)-(epsilon), where (epsilon) is the dimensionless viscosity. In the limit (epsilon)<<1 this rather weak energy dissipation leads only to insignificant distortion of the wave profile involved. So the solution obtained can be considered as a quasi-stationary wave for the rather long time of its propagation in a viscous medium.
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