Head-on collision between ion-acoustic (IA) multisolitons propagating in opposite directions in a magnetised spin quantum plasma having inertial ions and degenerate electrons with spin-up and spin-down states is studied. The extended Poincaré–Lighthill–Kuo (PLK) method is adopted to derive two Korteweg–de Vries (KdV) equations. Further, the Hirota bilinear method is employed to determine the soliton solutions of two KdV equations for single-soliton, double-soliton and triple-soliton cases. The analytical expressions of phase shift after head-on collision of IA multisolitons in different cases are also derived. The combined effects of different physical parameters such as spin-density polarisation, magnetic field and other physical parameters on the characteristics of IA solitons,and time evolution as well as phase shifts due to head-on collision between IA multisolitons have been numerically described. It is observed that the presence of spin-density polarisation awfully affects propagation properties of IA solitons and phase shifts for different cases. The results of the present investigation may be useful to understand the nonlinear features of a variety of nonlinear excitations in dense astrophysical plasma regions like white dwarfs.

The existence of the large-amplitude dust inertial Alfvén waves (DIAWs) has been presented in an electron-depleted, two-fluid dust-ion plasma. Linear analysis shows that the DIAWs travel slower than the dust Alfvén waves. DIAWs are the obliquely (with respect to the external magnetic field) propagating oscillations ofdust density, having the characteristics of a solitary wave. In order to observe the nonlinear behaviour of the DIAWs, the Sagdeev pseudopotential method has been used to derive the energy balance equation and from the expressionof the Sagdeev pseudopotential, the existence conditions for the DIAWs have also been determined. It is observed that density rarefactions travelling at sub- and super-Alfvénic speeds are associated with DIAWs.