Abstract
We present an investigation of nonlinear interactions between gravitational radiation and modified Alfv\'en modes in astrophysical dusty plasmas. Assuming that stationary charged dust grains form neutralizing background in an electron-ion-dust plasma, we obtain the three-wave coupling coefficients and calculate the growth rates for parametrically coupled gravitational radiation and modified Alfv\'en-Rao modes. The threshold value of the gravitational wave amplitude associated with convective stabilization is particularly small if the gravitational frequency is close to twice the modified Alfv\'en wave frequency. The implication of our results to astrophysical dusty plasmas is discussed.
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