Dissipative ion-acoustic solitary and shock waves in a plasma with superthermal electrons

The excitation of a nonlinear ion-acoustic (IA) wave packet in a viscous plasma consisting of superthermal electrons and cold ions is investigated. It is assumed that the superthermal components obey the Kappa distribution. The standard reductive perturbation technique is employed to obtain a cubic complex Ginzburg–Landau type equation, which governs the dynamics of the amplitude of IA wave packets in a viscous plasma. In a weakly dissipative regime, by means of a perturbation method adopted from non-integrable dynamical systems theory, explicit soliton solutions are obtained of the dissipative dynamical system, determined as fixed points of a two-dimensional system of evolution equations describing the soliton amplitude and velocity. The stability of bright solitons is addressed using adiabatic perturbation theory in a weakly dissipative case. In a general dissipation regime, a novel type of travelling solitary (dissipative solitons) and shock-type solutions are derived for an envelope equation. Moreover, the dependence of the solitary and shock wave characteristics on relevant physical parameters of the problem is studied. It is shown that dissipative solitons do exist, sustained by a mutual balance between loss and gain terms, in addition to the interplay between dispersion and nonlinearity. The dependence of solitary and shock wave velocities on the parameters of the system are investigated. To feature distinctive characteristics of a dissipative soliton, it is compared with the bright soliton solution of the nonlinear Schrödinger equation.