The dust-modified ion-acoustic waves of Shukla and Silin are revisited within the theoretical framework of the Tsallis statistical mechanics. Nonextensivity may originate from correlation or long-range plasma interactions. Interestingly, we find that owing to electron nonextensivity, dust ion-acoustic (DIA) solitary waves may exhibit either compression or rarefaction. Our analysis is then extended to include self-consistent dust charge fluctuation. In this connection, the correct nonextensive electron charging current is rederived. The Korteweg-de Vries equation, as well as the Korteweg-de Vries-Burgers equation, is obtained, making use of the reductive perturbation method. The DIA waves are then analyzed for parameters corresponding to space dusty plasma situations.

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Our recent analysis on nonlinear nonextensive dust-acoustic waves (DA) [Amour and Tribeche in Phys. Plasmas 17:063702, 2010] is extended to include selfconsistent nonadiabatic grain charge fluctuation. The appropriate nonextensive electron charging current is rederived based on the orbit-limited motion theory. Our results reveal that the amplitude, strength and nature of the nonlinear DA waves (solitons and shocks) are extremely sensitive to the degree of ion nonextensivity. Stronger is the electron correlation, more important is the charge variation induced nonlinear wave damping. The anomalous dissipation effects may prevail over that dispersion as the electrons evolve far away from their Maxwellian equilibrium. Our investigation may be of wide relevance to astronomers and space scientists working on interstellar dusty plasmas where nonthermal distributions are turning out to be a very common and characteristic feature.

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The combined effects of an oblique magnetic field and electron suprathermality on weak dust-acoustic (DA) waves in a charge varying electronegative dusty plasmas with application to the Halley Comet are investigated. The correct suprathermal electron charging current is derived based on the orbit-motion limited approach. A weakly nonlinear analysis is carried out to derive a Korteweg-de Vries-Burger equation. The electron suprathermality, the obliqueness, and magnitude of the magnetic field are found to modify the dispersive properties of the DA shock structure. Our results may aid to explain and interpret the nonlinear oscillations that may occur in the Halley Comet plasma.

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