A study is made of the stability of ion-acoustic solitons in a magnetized non-thermal plasma with warm ions. A Zakharov-Kuznetsov equation (KdV-ZK, or Korteweg-de Vries equation in three dimensions) is derived. This equation admits solutions representing compressive and rarefactive solitons propagating in any direction oblique to the external magnetic field. When the coefficient of the nonlinear term of this equation vanishes, the nonlinear behaviour of ion acoustic waves is described by a modified KdV-ZK (MKdV-ZK) equation, which is also derived. This equation also has solitarywave solutions. Finally, the three-dimensional stability of these solitons is investigated by the small-k perturbation expansion method of Rowlands and Infeld.

Dust ion-acoustic solitary structures have been investigated in an unmagnetized non-thermal plasma consisting of negatively charged dust grains, adiabatic positive ions, and non-thermal electrons. Whenever the non-thermal parameter exceeds a critical value, the present system supports negative potential double layer solution. However, this double layer solution is unable to restrict the occurrence of negative potential solitary waves of the present system. As a result, the occurrence of one type of negative potential solitary wave is restricted by Mc < M < MD, whereas the second type of solitary wave exists for all M > MD, where Mc is the lower bound of the Mach number M and MD (> Mc) is the Mach number corresponding to a negative potential double layer. A finite jump between the amplitudes of negative potential solitary waves at M = MD − ϵ1 and M = MD + ϵ2 has been observed, where 0 < ϵ1 < MD − Mc and ϵ2 > 0. Depending on the analytical theory presented in this paper, a numerical scheme has been provided to find the value of the Mach number at which double layer solution exists, and also the amplitude of that double layer. Although the occurrence of coexistence of solitary structures of both polarities is restricted by Mc < M ≤ Mmax, only negative potential solitary wave still exists for all M > Mmax, where Mmax is the upper bound of M for the existence of positive potential solitary waves only. Qualitatively different compositional parameter spaces showing the nature of existing solitary structures of the energy integral have been found. These solution spaces are capable of producing new results and physical ideas for the formation of solitary structures whenever one can move the solution spaces through the family of curves parallel to the curve M = Mc.

A computational scheme has been developed to study the arbitrary amplitude dust acoustic solitary waves and double layers in nonthermal plasma consisting of negatively charged dust grains, nonthermal ions, and isothermal electrons including the effect of dust temperature. The Sagdeev potential approach, which is valid to study the arbitrary amplitude solitary waves and double layers, has been employed. The computation has been carried out over the entire interval of β1:0≤β1&lt;βM. This β1 is a parameter associated with the nonthermal distribution of ions and βM is the upper bound of β1. Depending on the nature of existence of solitary waves and double layers, the interval for β1 can be broken up into four disjoint subintervals holding the other parameters fixed. By nature of existence of solitary waves and double layers, it is meant that in some subinterval only negative potential solitary waves can exist, whereas in another both negative and positive potential solitary waves can coexist along with a double layer, etc. Corresponding to every β1 lying within a subinterval of β1, there is a definite interval for the Mach number (definite value of the Mach number) for which there exists solitary waves (double layer) specific for that subinterval of β1. The role of dust temperature on the subintervals of β1 and on amplitude of solitary waves and double layers has been explored.

An evolution equation describing weakly nonlinear and weakly dispersive ion-acoustic waves in magnetized nonthermal plasma with warm ions, including the effect of Landau damping, has been derived. It is found that the coefficient of the nonlinear term of this equation vanishes along a particular curve in βσ-plane, where β is a parameter that determines the proportion of fast electrons and σ is the ratio of electron to ion temperature. In this case, the modified evolution equation has also been derived. The solitary wave solutions of these equations propagating obliquely to the external magnetic field have been obtained by the multiple time scale method. It has been found that in either case the amplitude of the solitary waves slowly decreases with time.

The Sagdeev potential technique has been employed to study the dust ion acoustic solitary waves and double layers in an unmagnetized collisionless dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, and isothermally distributed electrons and positrons. A