Abstract
Self-modulation instability in materials with hysteretic quadratic nonlinearity is analyzed theoretically. It is demonstrated that nonlinear attenuation specific to the materials with hysteretic quadratic nonlinearity does not prevent, in principle, the instability of a plane harmonic acoustic wave with respect to low-frequency modulating disturbances. However, nonlinear attenuation does narrow the frequency range and does diminish the space region where the development of self-modulation instability can take place. Nonlinear attenuation also causes diminishing of the modulation amplitude at some propagation distance from acoustic source even if initially it grows as a consequence of the instability.
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