Numerical simulation of dark envelope soliton in plasma

One-dimensional (1-D) particle-in-cell simulation is used to study the propagation of dark envelop solitons described by the nonlinear Schrodinger equation (NLSE) in electron-ion plasmas. The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the dark envelope soliton in plasma. It is demonstrated by our numerical simulation that there is dark envelope soliton in electron-ion plasmas. The numerical results are in good agreements with the analytical ones from the NLSE which is obtained from the reductive perturbation method. The limitation of the amplitude of dark envelop solitons in plasma is noticed.