A recent paper [L.-N. Hau and W.-Z. Fu, Phys. Plasmas 14, 110702 (2007)] deals with certain mathematical and physical properties of the kappa distribution. We comment on the authors’ use of a form of distribution function that is different from the “standard” form of the kappa distribution, and hence their results, inter alia for an expansion of the distribution function and for the associated number density in an electrostatic potential, do not fully reflect the dependence on $\kappa$ that would be associated with the conventional kappa distribution. We note that their definition of the kappa distribution function is also different from a modified distribution based on the notion of nonextensive entropy.

Dust ion acoustic solitons in an unmagnetized dusty plasma comprising cold dust particles, adiabatic fluid ions, and electrons satisfying a $\kappa$ distribution are investigated using both small amplitude and arbitrary amplitude techniques. Their existence domain is discussed in the parameter space of Mach number $M$ and electron density fraction $f$ over a wide range of values of $\kappa$ . For all $\kappa >3/2$ , including the Maxwellian distribution, negative dust supports solitons of both polarities over a range in $f$ . In that region of parameter space solitary structures of finite amplitude can be obtained even at the lowest Mach number, the acoustic speed, for all $\kappa$ . These cannot be found from small amplitude theories. This surprising behavior is investigated, and it is shown that $f_c$ , the value of $f$ at which the KdV coefficient $A$ vanishes, plays a critical role. In the presence of positive dust, only positive potential solitons are found.

The nonlinear propagation of ion-acoustic waves is considered in a magnetized plasma, composed of kappa distributed electrons and an inertial ion fluid. The fluid-dynamical system of equations governing the dynamics of ion-acoustic waves is reduced to a pseudoenergy-balance equation. The properties of arbitrary amplitude, obliquely propagating ion-acoustic solitary waves are thus investigated via a mechanical-motion analog (Sagdeev potential) approach. The presence of excess superthermal electrons is shown to influence the nature of magnetized ion-acoustic solitons. The influence on the soliton characteristics of relevant physical parameters such as obliqueness (the angle between soliton propagation direction and magnetic field), the electron deviation from a Maxwellian (“superthermality”) and the soliton speed is investigated.

Velocity distribution functions with an excess of superthermal particles are commonly observed in space plasmas, and are effectively modeled by a kappa distribution. They are also found in some laboratory experiments. In this paper we obtain existence conditions for and some characteristics of ion-acoustic solitary waves in a plasma composed of cold ions and $\kappa$ -distributed electrons, where $\kappa >3/2$ represents the spectral index. As is the case for the usual Maxwell–Boltzmann electrons, only positive potential solitons are found, and, as expected, in the limit of large $\kappa$ one recovers the usual range of possible soliton Mach numbers, viz., $1<M<1.58$ . For lower values of $\kappa$ , modeling the presence of a greater superthermal component, the range of accessible Mach numbers is reduced. It is found that the amplitude of the largest possible solitons that may be generated in a given plasma (corresponding to the highest allowed Mach number for the given plasma composition) falls off with decreasing $\kappa$ , i.e., an increasing superthermal component. On the other hand, at fixed Mach number, both soliton amplitude and profile steepness increase as $\kappa$ is decreased. These changes are seen to be important particularly for $\kappa <4$ , i.e., when the electrons have a “hard” spectrum.

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrödinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.

Abundant evidence for the occurrence of modulated envelope plasma wave packets is provided by recent satellite missions. These excitations are characterized by a slowly varying localized envelope structure, embedding the fast carrier wave, which appears to be the result of strong modulation of the wave amplitude. This modulation may be due to parametric interactions between different modes or, simply, to the nonlinear (self-)interaction of the carrier wave. A generic exact theory is presented in this study, for the nonlinear self-modulation of known electrostatic plasma modes, by employing a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The (moderately) nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrödinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright-(pulses) or dark- (holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness (with respect to the propagation direction), finite temperature and defect (dust) concentration are explicitly considered. Relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.