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

Abstract

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.

Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber

“…Furthermore, Eq. (12) also exhibits stationary solutions for finite ξ and α = 0 in the form of a chirped traveling solution [19].…”

“…Then, motivated by the analytical results of [17][18][19], we look for solutions of Eq. ( 12) with a nonnegligible right-hand side and with both nonzero ξ and nonzero α in the form…”

Dissipative solitons in an atomic medium assisted by an incoherent pumping field

“…In a recent study, Facão and co-workers have investigated the existence of temporal optical dissipative solitons in a gas-filled fiber with a 3-level atomic media [32]. The family of solutions proposed is an extension of those previous predicted in the literature for cases where β i p = 0 [39], and are given by…”

“…We apply the standard multiscale perturbation technique [15] to derive an effective one-dimensional Cubic Ginzburg-Landau equation (CGLE), which describes the dynamics of the envelope of a pulsed probe beam. In section III, we introduce the solutions for temporal dissipative solitons previously proposed in the literature [32,39] and in section IV we explore the role of the incoherent pumping for controlling the linear and nonlinear optical properties and the gain and loss processes. After the correct choice of the parameters, in section V we test a family of dissipative solitons by performing both numerical simulations of the (1+1)-dimensional effective model but also of the Maxwell-Bloch system.…”

Localized structures in complex plasmas in the presence of a magnetic field

“…The MI in DNLS-like lattices was first predicted in the first Brillouin zone (Christodoulides and Joseph 1988) and experimental observation of discrete MI has been reported for the first time by Meier et al (2004). The study of MI is essential as it stands as a precursor phenomenon to the formation of discrete soliton (Braun and Kivshar 1998;Henning and Tsironis 1999). The MI appears in the same parameter region where solitons are observed (Rajib et al 2015).…”