Modulational instability of quantum electron-acoustic waves and associated envelope solitons in a degenerate quantum plasma

Abstract: The basic features of linear and nonlinear quantum electron-acoustic (QEA) waves in a degenerate quantum plasma (containing non-relativistically degenerate electrons, superthermal or $\kappa$-distributed electrons, and stationary ions) are theoretically investigated. The nonlinear Sch\"{o}dinger (NLS) equation is derived by employing thereductive perturbation method. The stationary solitonic solution of the NLS equation are obtained, and examined analytically as well as numerically to identify the basic features of the QEA envelope solitons. It has been found that the effects of the degeneracy and exchange/Bohm potentials of cold electrons, and superthermality of hot electrons significantly modify the basic properties of linear and nonlinear QEA waves. It is observed that the QEA waves are modulationally unstable for $k<k_c$, where $k_c$ is the maximum (critical) value of the QEA wave number $k$ below which the QEA waves are modulationally unstable), and that for $k<k_c$ the solution of the NLS equation gives rise to the bright envelope solitons, which are found to be localized in both spatial ($\xi$) and time ($\tau$) axes. It is also observed that as the spectral index $\kappa$ is increased, the critical value of the wave number (amplitude of the QEA envelope bright solitons) decreases (increases). The implications of our results should be useful in understanding the localized electrostatic perturbation in solid density plasma produced by irradiating metals by intense laser, semiconductor devices, microelectronics, etc.