Abstract
This study is essentially an attempt to investigate the effects of trapped ions concentration on the dynamics of dust-acoustic (DA) periodic travelling waves in dusty plasmas, which consist of dust fluid, trapped ions, and Maxwellian electrons. The physical nature of DA solitary and periodic travelling waves in the plasma model at hand is governed by a Korteweg-de Vries (KdV) type equation. Bifurcation analysis of the Hamiltonian system is applied to demonstrate the probability of the presence of DA solitary and periodic travelling waves for the KdV type equation. A careful discussion illustrates that non-linear phenomena of DA solitary and periodic travelling waves are modified due to the presence of the trapped ions concentration. It is found numerically that the negative amplitude of DA periodic travelling waves is amplified, as the trapping parameter that determines the number of the trapped ions is increased. The numerical simulation gives rise to significant highlights on the dynamics of solitary and periodic travelling waves in astrophysical environments such as Saturn's moon Enceladus.