The theoretical investigation of shocks and solitary structures in a dense quantum plasma containing electrons at finite temperature, nondegenerate cold electrons, and stationary ions has been carried out. A linear dispersion relation is derived for the corresponding electron acoustic waves. The solitary structures of small nonlinearity have been studied by using the standard reductive perturbation method. We have considered collisions to be absent, and the shocks arise out of viscous force. Furthermore, with the help of a standard reductive perturbation technique, a KdV–Burger equation has been derived and analyzed numerically. Under limiting cases, we have also obtained the KdV solitary profiles and studied the parametric dependence. The results are important in explaining the many phenomena of the laser–plasma interaction of dense plasma showing quantum effects.
Modulation instability (MI) of envelope soliton is studied in an unmagnetized viscous plasma. Using Krylov-Bogoliubov Mitropolsky (KBM) method, the nonlinear Schrödinger equation (NLSE) is obtained, and the growth rate of modulationally unstable electron acoustic wave in such plasma is discussed. The solution of the electron-acoustic envelope-solitons is obtained from the Nonlinear Schrödinger equation. The hypothetical outcomes have been examined mathematically for various parameters of plasma, and the outcomes are introduced graphically. This theoretical investigation can be experienced experimentally with certain modification of the experiment had been performed by Ikezawa and Nakamura []. Our outcomes might be material for the investigation of nonlinear wave measures in relativistic thick plasmas of astrophysical articles, to be specific, in dwarfs and neutron stars.
The propagation of electron acoustic solitary waves is investigated in magnetized two‐temperature electron plasma with supra‐thermal ion. By using the reductive perturbation technique, the Korteweg de‐Vries (KdV) equation is derived. Later solving this equation, a solitary wave solution has been derived. These are mainly in astrophysical plasmas where changes of local charge density, temperature, and energy of particles produce considerable effects on the plasma system. The effects of supra‐thermality, density, and Mach number on solitary structures are studied in detail. The results show that the supra‐thermal index (κ) and ion to electron temperature ratio (σ) alters the regime where solitary waves may exist. While studying the solitary profile for different parametric variation some interesting conclusion can be drawn; it is shown that the solitary profile becomes flatter. This can be due to the thermal energy associated with the hot electrons. However, with the increase in ion density with respect to the cold electrons' density, the solitary waves become steeper and sharper. This is due to the comparatively heavier mass of ions. The density of cold electron also increases the solitary structures in a similar manner. The higher the density of cold electrons, sharper will be the profile. The above findings will be helpful in understanding many astrophysical phenomena and data obtained by space missions. For a further study, we keep the investigation of the formation of other kinds of stationary structures like shocks, double layers, etc.
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