Supercritical dynamics of magnetoelastic wave triad in a solid

Parametric coupling of three traveling waves is studied numerically on an example of magnetoelastic waves in a highly anharmonic antiferromagnetic crystal. The physical mechanism of coupling is explained as a result of modulation of the nonlinear elastic moduli of the crystal by RF electromagnetic pumping. Parametric interaction of a coupled wave triad with homogeneous pumping field results in an instability of explosive type. Above the threshold of instability, the amplitudes of waves increase to occurrence of singularity in finite time. Explosion is accompanied by spatial localization of wave envelopes. The supercritical dynamics of a wave triad is simulated numerically taking into account the third- and fourth-order magnetoelastic anharmonicity of the medium. Violation of the explosive scenario by nonlinear phase mismatch between the coupled waves and pumping field is demonstrated. Modulation of the pumping phase in time is considered as a tool to compensate for the nonlinear mismatch and recondition the explosive amplification and spatial localization of wave triads. A proper phase modulation law is found in a numerical experiment.