Effects of linear and nonlinear resonances on dust-acoustic solitary waves in an opposite polarity dusty plasma with generalized polarization force

The linear resonance (Landau damping) and nonlinear resonance (trapping) effects on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in an opposite polarity unmagnetized collisionless dusty plasma in the presence of generalized polarization force. The two-species of multiply charged dust grains (positive and negative) are described by the kinetic Vlasov equations, whereas the inertialess ions and electrons are described by Maxwellian distribution. Using the multi-scale reductive perturbation technique generalized for the applications to the Vlasov equation, we derive two modified Korteweg–de Vries (KdV) equations that govern the evolution of DASWs with the effects of linear resonance (Landau damping) and nonlinear resonance (trapping), respectively. It is found that the KdV soliton theory modified by the effects of nonlinear resonant particles is not applicable to the small amplitude limit of DASWs. The properties of the phase velocity, solitary wave amplitudes (in the presence and absence of Landau damping), and the Landau damping rate of DASWs are studied with the effects of generalized polarization force ( ∝R), the ratios of the positive to negative dust charge numbers z, ion to positively (negatively) charged dusts temperatures σp (σn), as well as the negatively to positively charged dusts mass (m). The properties of the decay rates of the amplitude of the KdV soliton with a small effect of Landau damping are also studied with the above system of parameters. It is shown that the decay rate of the wave amplitude is reduced by the effects of R. In addition, the competition between the linear and nonlinear resonances on the system parameters has been discussed. It is observed that the nonlinear resonance effects are relatively higher than those of the linear one under the generalized polarization force, although they are comparable in magnitude in the absence of the polarization force. The implications of the present investigation in different dusty plasma environments are briefly discussed. The results may be useful for understanding the localization of solitary pulses and associated resonance damping of the wave in laboratory and space plasmas, in which the positively and negatively charged dusts coexist under the polarization force.