Characteristics of dust acoustic waves in dissipative dusty plasma in the presence of trapped electrons

The formation and propagation of nonlinear dust acoustic waves (DAWs) as solitary and solitary/shock waves in an unmagnetized, homogeneous, dissipative and collisionless dusty plasma comprising negatively charged micron sized dust grains in the presence of free and trapped electrons with singly charged non-thermal positive ions is discussed in detail. The evolution characteristics of the solitary and shock waves are studied by deriving a modified Korteweg–de Vries–Burgers (mKdV–Burgers) equation using the reductive perturbation method. The mKdV–Burgers equation is solved considering the presence (absence) of dissipation. In the absence of dissipation the system admits a solitary wave solution, whereas in the presence of dissipation the system admits shock waves (both monotonic and oscillatory) as well as a combination of solitary and shock wave solutions. Standard methods of solving the evolution equation of shock (solitary) waves are used. The results are discussed numerically using standard values of plasma parameters. The findings may be useful for better understanding of formation and propagation of waves in astrophysical plasma.