Polarization- and self-gravity-modulated nonlinear periodic waves in superthermal dusty plasmas

Abstract This paper investigates dust-acoustic waves in a polarized, self-gravitating dusty plasma with kappa-distributed superthermal ions. We resolve the longstanding degeneracy in the common Ψ = ΓΦ assumption by demonstrating that polarization and self-gravity, though mathematically coupled, exert physically distinct influences on wave dynamics. Linear analysis reveals that polarization actively suppresses wave propagation, while self-gravity controls Jeans instability thresholds; their competition creates tunable stability boundaries scalable with plasma parameters. Through reductive perturbation theory, we derive a gravitationally modified Korteweg–de Vries equation whose coefficients explicitly depend on polarization strength R , self-gravity parameter (Γ), and ion superthermality κ i . Analytical solutions obtained via the ( g ′/ g ) expansion method yield a spectrum of coherent structures, including bright solitons, kinks, and singular waves. The joint modification of wave propagation arises from a scale-dependent competition: self-gravity acts as a long-range attractive force that reduces phase velocity and fosters clumping, while the polarization force provides a repulsive correction sensitive to plasma gradients. The physical mechanism is driven by ion superthermality; a lower spectral index κ i provides a more energetic ion population that more easily deforms the Debye shielding cloud around dust grains, thereby strengthening the polarization force and intensifying nonlinear steepening. Strong ion superthermality (lower κ i ) amplifies both mechanisms by increasing the polarization coefficients <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:mrow> </m:msub> </m:math> ${c}_{{\kappa }_{1}}$ , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:mrow> </m:msub> </m:math> ${c}_{{\kappa }_{2}}$ and reducing the effective Jeans length, thereby promoting the formation of persistent, macroscopic structures. These results provide a unified mechanism to explain transient “spokes” in Saturn’s rings and initial dust clumping in protoplanetary disks, bridging grain-scale interactions to collective astrophysical phenomena.