Self-modulation instability in materials with hysteretic quadratic nonlinearity

Self-modulation instability in materials with hysteretic quadratic nonlinea rity is analyzed theoretically. It is demonstrated that nonlinear attenuati on specific to the materials with hysteretic quadratic nonlinearity does no t prevent, in principle, the instability of a plane harmonic acoustic wave with respect to low-frequency modulating disturbances. However, nonlinear a ttenuation does narrow the frequency range and does diminish the space regi on where the development of self-modulation instability can take place. Non linear attenuation also causes diminishing of the modulation amplitude at s ome propagation distance from acoustic source even if initially it grows as a consequence of the instability. (C) 2001 Elsevier Science B.V. All right s reserved.