Quantitative analysis of modulational instability in Yukawa fluids

We present a comprehensive quantitative analysis of the modulational instability of dust-acoustic waves across a broad parametric space in strongly coupled Yukawa fluids. Using fluid equations supplemented by an appropriate equation of state, we employ the reductive perturbation technique to derive the nonlinear Schrödinger equation and establish the modulational instability conditions. Our formulation effectively predicts the critical values of the coupling parameter Γ and the screening parameter κ on modulational instability in Yukawa fluid excitations. More quantitatively, Yukawa fluid excitations for carrier wave numbers k≳0.25 become modulationally stable beyond Γ∼6.0 for κ≳0.2, while for k≲0.25, instability persists in the long-range interaction regime (κ∼0.06–0.1) even at large Γ. The instability region in κ-space also broadens with increasing k, indicating stronger sensitivity to screening at relatively shorter wavelengths. A comprehensive analysis of modulational instability is presented across the experimentally accessible Γ–κ parameter space, providing deeper insight into stability across realistic coupling and screening regimes. Moreover, the present model successfully overcomes the limitations of existing approaches, such as the nonlinear quasi-localized charged approximation and generalized hydrodynamic models, in accurately describing modulational instability in Yukawa fluids.