Ion-acoustic waves (IAWs) are investigated in an unmagnetized collisionless plasma comprising dynamical ions and inertialess cold and hot (C-H) electrons expressed by Maxwellian, kappa, and (r,q) distributions. The reductive perturbation theory is applied for deriving a modified Kadomtsev-Petviashvili (mKP) equation to examine the characteristics of ion-acoustic structures (solitary waves). The Hirota bilinear formalism is used to investigate the propagation of a single soliton and the interaction of two solitons with special reference to space plasmas. It is found that ratio of number density of cold to hot electrons and non-Maxwellian nature of cold electrons not only affect the propagation characteristics of single mKP solitons but also alter the interaction time of the IASWs. It is found that the swiftness of the interaction of solitons for flat-topped distribution surpasses both kappa and Maxwellian distributions. It is also found that the bipolar and tripolar structures depend on the ratio of the propagation vectors. The ranges of electric field amplitude for the IASWs are calculated for C-H electrons distributions corresponding to Saturn's B-ring and the region just beyond terrestrial magnetopause, and are shown to agree with Cassini Wideband Receiver (WBR) observational data and Wideband plasma wave instrument's waveform data.
The nonlinear characteristics of dust-acoustic (DA) structures including the localized and periodic waves in a plasma having Maxwellian ions and superthermal two-temperature electrons are investigated. The wave equations including both Kadomtsev-Petviashvili (KP) and modified KP (mKP) equations are derved using the reductive perturbation technique (RPT). The quantitative and qualitative characteristics of both compressive and rarefactive structures are studied. Jacobi elliptic function expansion method (JEFEM) is employed for the purpose of quantitative analysis while the qualitative behavior is studied by dint of the dynamical system approach. The solutions to the mKP equation hold at a critical condition where the quadratic nonlinearity ceases to exist. It is noticed that the KP equation admits only rarefactive solitary waves (SWs) whereas the mKP equation admits both compressive and rarefactive SWs. It is found that the profile (amplitude and width) of both DA solitary and periodic structures are different at different radii of Saturn's inner magnetosphere. The effect of kappa spectral index is studied and it is found that when the population of energetic cold electrons is decreased, the solitary structure gets energized. Our study is applied to Saturn's inner magnetosphere where kappa distributed two-temperature electrons and dust grains with gegative charge are observed by various satellite missions.
Dust ion acoustic waves (DIAWs) are analysed in multi‐component plasmas via reductive perturbation technique comprising inertial ions, (r, q) distributed electrons, and stationary dust by using fluid theory of plasmas. The modified Kadomtsev‐Petviashvili (MKP) equation is obtained for the critical condition at which the quadratic nonlinearity vanishes. Hirota's bilinear formalism is employed, for the first time, to study the two‐soliton solutions of MKP equation in the context of plasma physics. The effects of flatness at low energy (represented by r) and superthermality at high energy (represented by q) of electrons in phase space are investigated for the linear and nonlinear propagation of DIAWs. It is found that the amplitude of the nonlinear DIAW is highest for the flat‐topped distribution, whereas it is lowest for kappa distribution. Using the plasma parameters of Saturn's B‐ring. The estimates are given of the spatial scales over which the MKP solitons form for flat‐topped, kappa, and Maxwellian distributions, respectively. It is also discussed in detail how the presence of dust and non‐Maxwellian electron distributions affect the interaction of MKP solitons in Saturn's B‐ring. In addition, the interaction of a compressive and rarefactive soliton is studied giving results not achievable for KdV and KP equations.
Motivated by the observations of Voyager 1 and 2 spacecraft and Freja satellite observations in Saturn’s magnetosphere, the formation of dust-acoustic (DA) localized and periodic waves in a complex plasma having superthermal electrons and ions are reported. In this regard, a modified Kadomtsev–Petviashvili (mKP) equation is derived by employing the weak turbulence theory for studying the characteristics of the nonlinear dust-acoustic waves (DAWs) in the model under consideration. The localized and periodic wave solutions to the mKP equation are derived using ansatz method in terms of Jacobi elliptic functions (JEFs). It is reported that the phase velocity of the DAWs in the Saturn’s magnetosphere is lower for kappa distributed ions and electrons by comparison with regions of space plasmas where the electrons and ions follow the Maxwellian distribution. The conditions for the existence of both localized and periodic waves are also presented. Estimates are also given of the spatial scales over which the dust-acoustic solitary/periodic structures form in Saturn’s magnetosphere.
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