Head-on collision among dust acoustic (DA) multi-solitons in a dusty plasma with ions featuring non-Maxwellian hybrid distribution under the effect of the polarization force is investigated. The presence of the non-Maxwellian ions leads to eloquent modifications in the polarization force. Specifically, an increase in the superthermality index of ions (via κi) and nonthermal parameter (via α) diminishes the polarization parameter. By employing the extended Poincaré-Lighthill-Kuo method, two sided KdV equations are derived. The Hirota direct method is used to obtain multi-soliton solutions for each KdV equation, and all of them move along the same direction where the fastest moving soliton eventually overtakes the others. The expressions for collisional phase shifts after head-on collision of two, four, and six-(DA) solitons are derived under the influence of polarization force. It is found that the effect of polarization force and the presence of non-Maxwellian ions have an emphatic influence on the phase shifts after the head-on collision of DA rarefactive multi-solitons. In a small amplitude limit, the impact of polarization force on time evolution of multi-solitons is also illustrated. It is intensified that the present theoretical pronouncements actually effectuate in laboratory experiments and in space/astrophysical environments, in particular in Saturn's magnetosphere and comet tails.

An investigation of dust ion-acoustic (DIA) cnoidal waves in unmagnetized collisionless plasma consisting of two temperature superthermal electrons, inertial warm ions, and negatively charged dust grains is presented. Reductive perturbation technique has been used to derive the modified Korteweg-de Vries (mKdV) equation for the study of nonlinear periodic waves. Further, applying the Sagdeev potential approach, energy balance equation is derived. Using the expression for Sagdeev potential in expanded form, the cnoidal wave solution is determined. Both positive and negative potential (compressive and rarefactive) nonlinear DIA cnoidal structures are observed. The effects of parameters like the number density of cold electrons, superthermality of hot and cold electrons, ions to hot electrons temperature ratio, and dust to ion density ratio on the characteristics of DIA cnoidal waves are analyzed.

An investigation of heavy nucleus-acoustic (HNA) excitations in a degenerate relativistic magnetorotating quantum plasma system comprising relativistically degenerate light nuclei/electrons and inertial nondegenerate heavy nuclei has been presented. The Zakharov-Kuznetsov-Burgers (ZKB) equation has been derived by employing the reductive perturbation method. The solution of the ZKB equation supports only positive potential monotonic and oscillatory HNA shock waves in congruence with the space observations. It is observed that the heavy nucleus viscosity is a source of dissipation and is responsible for the formation of HNA monotonic and oscillatory shock structures. Bifurcation analysis is also examined in the absence of dissipation. It is shown that the combined effects of external magnetic field strength, rotational frequency, and obliqueness significantly modify the basic properties of different HNA nonlinear structures. The results should be utilitarian to understand the characteristics of nonlinear excitations in degenerate relativistic magnetorotating quantum plasma which is present in astrophysical compact objects especially in white dwarfs and neutron stars.

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