Soliton reflection in a plasma with trapped electrons: The effect of dust concentration

Considering an inhomogeneous plasma that has trapped electrons and dust grains, we investigate the possible modes, their evolution as solitons and the reflection of solitons from the density gradient. The usual form of the Korteweg–de Vries (KdV) equation, which governs the behaviour of solitons, is modified for the present plasma, and is solved by finding appropriate transformations. The role of the charge Z d (positive: α = + 1 or negative: α = − 1 ) of the dust and dust concentration n d 0 in the presence of trapped electrons (density n e l 0 and temperature T e l 0 ) is investigated for the soliton reflection. The mode that evolves as a soliton can propagate in the plasma only when ion temperature T i ≥ α n d 0 Z d / ( n e h 0 T e h + n e l 0 T e l ) , where n e h 0 and T e h 0 are the density and temperature of nonisothermal electrons. Only the compressive solitons are found to propagate and reflect in the plasma (along with a shift) when the dust charge density remains smaller than the total charge density of the electrons of both types.