Existence of dust ion acoustic solitary wave and double layer solution at M = Mc

TL;DR

This paper investigates dust ion acoustic solitary waves and double layers at the acoustic speed in a dusty plasma, revealing conditions for their existence, polarity, and the occurrence of supersolitons through the Sagdeev potential method.

Contribution

It provides a detailed parameter space analysis showing the existence and polarity of solitary structures and introduces the concept of supersolitons at the acoustic speed.

Findings

Negative potential double layer exists along a specific curve in parameter space.

Negative potential supersolitons can occur beyond the double layer region.

Amplitudes of solitary structures are affected by plasma parameters.

Abstract

The Sagdeev potential technique has been used to investigate the existence and the polarity of dust ion acoustic solitary structures in an unmagnetized collisionless nonthermal dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions and nonthermal electrons when the velocity of the wave frame is equal to the linearized velocity of the dust ion acoustic wave for long wave length plane wave perturbation, i.e., when the velocity of the solitary structure is equal to the acoustic speed. A compositional parameter space has been drawn which shows the nature of existence and the polarity of dust ion acoustic solitary structures at the acoustic speed. This compositional parameter space clearly indicates the regions for the existence of positive and negative potential dust ion acoustic solitary structures. Again, this compositional parameter space shows that the present system supports the negative potential double layer at the acoustic speed along a particular curve in the parametric plane. However, the negative potential double layer is unable to restrict the occurrence of all negative potential solitary waves. As a result, in a particular region of the parameter space, there exist negative potential solitary waves after the formation of negative potential double layer. But the amplitudes of these supersolitons are bounded. A finite jump between amplitudes of negative potential solitons separated by the negative potential double layer has been observed, and consequently, the present system supports the supersolitons at the acoustic speed in a neighbourhood of the curve along which negative potential double layer exist. The effects of the parameters on the amplitude of the solitary structures at the acoustic speed have been discussed.