Dust acoustic solitary waves and double layers in a dusty plasma with trapped electrons

The effect of variable dust charge, dust temperature, and trapped electrons on small amplitude dust acoustic waves is investigated. It is found that both compressive and rarefactive solitons as well as double layers exist depending on the nonisothermality parameter. A modified Korteweg–de Vries is derived. At critical density, the Korteweg–de Vries equation is obtained. Employing quasipotential analysis, the Sagdeev potential equation with the inclusion of different new effects has been derived. Because of the presence of free and trapped electrons, the plasma acoustic wave has gained features of various solitary waves. The Sagdeev potential equation, at a small amplitude, shows that the ordering of nonisothermality plays a unique role. In the case of a plasma with first-order nonisothermality, the Sagdeev potential equation shows the compressive solitary wave propagation, while for plasma with higher-order nonisothermality, the solution of this equation reveals the coexistence of both compressive and rarefactive solitary waves. In addition, for certain plasma parameters, the solitary wave disappears and a double layer is expected. Again, with the better approximation in the Sagdeev potential equation, more features of solitary waves, e.g., spiky and explosive, along with the double layers, are also highlighted. The findings of this investigation may be useful in understanding laboratory plasma phenomena and astrophysical situations.