Growth rate and wave frequency of weakly two-dimensional nonlinear waves in dusty plasmas

Abstract This paper investigates the nonlinear modulation and stability of weakly two-dimensional wave packets in dusty plasmas, aiming to clarify the influence of multidimensional effects on wave evolution and frequency modulation. Employing the Davey–Stewartson (DS) equation for dust acoustic wave (DAW) dynamics, we analytically derived the dispersion relation and modulational instability conditions. Furthermore, the dependence of growth rate and modulation frequency on the wave number, density ratio, and temperature ratio is quantified. It is found that shorter waves boost frequency and instability (moderate k max). Higher electron-dust density raises frequency but suppresses instability; higher ion temperature weakens instability but lifts the high- k frequency. These findings enrich the theoretical framework for nonlinear wave modulation in dusty plasmas and guide plasma experimental diagnostics and stability control.