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.

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A general theory for the existence of solitary structure at M = Mc has been discussed, where Mc is the lower bound of the Mach number M, i.e., solitary structures start to exist for M > Mc. Three important results have been proved to confirm the existence of solitary structure at M = Mc. If V(φ)(≡ V(M,φ)) denotes the Sagdeev potential with φ being the perturbed field or perturbed dependent variable associated with a specific problem, V(M, φ) is well defined as a real number for all M ∈ ℳ and φ ∈ Φ0, and V(M, 0) = V′(M, 0) = V″(Mc, 0) = 0, V‴(Mc, 0) < 0 (V‴(Mc, 0) > 0), ∂ V/∂ M < 0 for all M (∈ ℳ) > 0 and φ (∈ Φ0) > 0 (φ (∈ Φ0) < 0), where ‘′ ≡ ∂/∂φ’, the main analytical results for the existence of solitary wave or double layer solution of the energy integral at M = Mc are as follows. Result 1: If there exists at least one value M0 of M such that the system supports positive (negative) potential solitary waves for all Mc < M < M0, then there exists either a positive (negative) potential solitary wave or a positive (negative) potential double layer at M = Mc. Result 2: If the system supports only negative (positive) potential solitary waves for M > Mc, then there does not exist positive (negative) potential solitary wave at M = Mc. Result 3: It is not possible to have coexistence of both positive and negative potential solitary structures at M = Mc. Apart from the conditions of Result 1, the double layer solution at M = Mc is possible only when there exists a double layer solution in any right neighborhood of Mc. Finally, these analytical results have been applied to a specific problem on dust acoustic (DA) waves in non-thermal plasma in search of new results.

Large amplitude dust acoustic solitary waves and double layers in a nonthermal plasma consisting of positively charged dust grains, nonthermal electrons, and isothermal ions including the effect of dust temperature have been studied using the Sagdeev potential technique by a computational scheme. The effect of different parameters on the nature of existence of solitary waves and double layers has been investigated to delimit their compositional parameter space. The physics corresponding to the computational result has been pointed out.