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Dust acoustic solitary waves, blow-up solitary waves and periodic waves have been investigated in unmagnetized dusty plasmas with Maxwell-distributed electrons and ions, considering dust charge fluctuations using the bifurcation theory of planar dynamical systems. The basic equations are transformed to an ordinary differential equation involving the electrostatic potential. Applying the bifurcation theory of planar dynamical systems, we have established the existence of solitary, blow-up solitary and periodic waves. Four exact solutions of the solitary, blow-up solitary and periodic waves are derived depending on the physical parameters. Regarding the solitary, blow-up solitary and periodic waves, we have presented the combined effects of the density ratio of electrons and ions (
), the temperature ratio of electrons and ions
and the speed of the travelling wave (
) on the characteristics of dust acoustic solitary, blow-up solitary and periodic waves.
Ion acoustic solitary waves and periodic waves in an unmagnetized plasma with superthermal (kappa-distributed) electrons and positrons are investigated through a non-perturbative approach. Model equations are transformed to a planar dynamical system. Then by using the bifurcations of phase portraits of this planar dynamical system, we have established that our model has solitary wave and periodic wave solutions. We have obtained two analytical solutions for these solitary and periodic waves depending on the parameters. From these solitary wave and periodic wave solutions, we have shown the combined effects of temperature ratio (σ) of electrons and positrons, spectral index (κ), speed of the traveling wave (v), and density ratio (p) of positrons and electrons on the characteristics of ion acoustic solitary and periodic waves. The spectral index, density ratio, speed of the traveling wave, and temperature ratio significantly affect the characteristics of ion acoustic solitary and periodic structures. The present study might be helpful to understand the salient features of nonlinear ion acoustic solitary and periodic structures in the interstellar medium.
The head-on collision between two cylindrical/spherical ion acoustic solitary waves (IASWs) in un-magnetized plasmas comprising inertial ions and q-non-extensive electrons and positrons is investigated using the extended version of the Poincaré–Lighthill–Kuo perturbation method. How the interactions are taking place in cylindrical and spherical geometry are studied, and the collision is shown at different times. The non-planar geometry can modify analytical phase shifts following the head-on collision are derived. The effects of q-non-extensive electrons and positrons on the phase shift are studied. It is shown that the properties of the interaction of IASWs in cylindrical and spherical geometry are very different.
The properties of non-planar (cylindrical and spherical) dust-acoustic solitary waves (DA SWs) and double layers (DLs) in an unmagnetised collisionless four-component dusty plasma, whose constituents are positively and negatively charged dust grains, super thermal electrons and Boltzmannian ions are investigated by deriving the modified Gardner (MG) equation. The well known reductive perturbation method is employed to derive the MG equation and solve it numerically to study the nonlinear features of the finite amplitude non-planar DA Gardner solitons (GSs) and DLs, which are shown to exist for κ around its critical value κc (where, κ is the super thermal parameter and κc is the value of κ corresponding to the vanishing of the nonlinear coefficient of the Korteweg-de Vries (K-dV) equation). It is seen that the properties of non-planar DA SWs and DLs are significantly differs in non-planar geometry from planar geometry. It is also found that the magnitude of the amplitude of positive and negative GSs decreases with κ and the width of positive and negative GSs increases with the increase of κ.
The head-on collision between two magneto-acoustic solitons in spin-1/2 fermionic quantum plasma is studied in the framework of the model proposed by Marklund et al. (Marklund, M., Eliasson, B. and Shukla, P. K. 2007 Phys. Rev. E. 76, 067401). The extended Poincare–Lighthill–Kuo method is used to obtain the phase shifts and the trajectories during the head-on collision of two solitons. The effect of the Zeeman energy for different speeds of the waves, the effect of the total mass density of the charged plasma particles for different strengths of magnetic field, the effect of the speed of the wave for different values of the Zeeman energy, and that of the ratio of the sound speed to Alfven speed for different values of Zeeman energ on the phase shift are studied. It is observed that the phase shifts are significantly affected in all the cases. The most interesting observation of this paper is that the phase shifts increase as well as decrease, and also they may be positive as well as negative depending upon the domain of the chosen parameters.
The properties of non-planar (cylindrical and spherical) ion acoustic solitary waves (IASWs) in an unmagnetized collisionless electron-positron-ion (e-p-i) plasma, whose constituents are inertial ions and superthermal/non-Maxwellian electrons and positrons (represented by the kappa (κ) distribution), are investigated by deriving the modified Gardner (MG) equation. The well-known reductive perturbation method is employed to derive the MG equation. The basic features of non-planar IA Gardner solitons (GSs) are discussed. It is seen that the properties of non-planar IAGSs (positive and negative) differ significantly as the value of spectral index kappa changes.
Recently Mace et at. studied electron-acoustic solitary waves in a plasma using a pseudopotential approach. To find the finite ion-temperature Sagdeev potential, they used a numerical technique developed by Baboolal, Bharuthram & Hellberg. In this paper we show that the exact pseudopotential can be obtained in this case in an analytical form. The numerical results obtained by Mace et at. are compared with our result, and complete agreement is found. We also discuss the conditions for the existence of solitary-wave solutions, and obtain the soliton solutions in some cases when these conditions are satisfied.
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