A theoretical and numerical investigation has been carried out on amplitude modulated heavy nucleus-acoustic envelope solitons (HNAESs) in a degenerate relativistic quantum plasma (DRQP) system containing relativistically degenerate electrons and light nuclei, and non-degenerate mobile heavy nuclei. The cubic nonlinear Schrödinger equation, describing the nonlinear dynamics of the heavy nucleus-acoustic waves (HNAWs), is derived by employing a multi-scale perturbation technique. The dispersion relation for the HNAWs is derived, and the criteria for the occurrence of modulational instability of the HNAESs are analyzed. The localized structures (viz., envelope solitons and associated rogue waves) are found to be formed in the DRQP system under consideration. The basic features of the amplitude modulated HNAESs and associated rogue waves formed in realistic DRQP systems are briefly discussed.

[1] The possibility for the formation of the dust-ion-acoustic (DIA) double layers (DLs) in a four-component dusty nonthermal plasma (containing nonthermal electrons, inertial ions, and stationary positively as well as negatively charged dust) has been theoretically investigated by deriving a modified Gardner (MG) equation. The latter has been numerically analyzed in order to identify the basic features of the nonplanar (cylindrical and spherical) DIA DLs. The DIA DLs (that are shown to be associated only with negative potential) have been found to exist for a suitable value of a or m, where a (m) is the parameter determining the number of nonthermal electrons (net dust charge density) in the plasma system under consideration. The implications of our results in some space dusty plasma environments have been discussed.Citation: Mamun, A. A., and S. Islam (2011), Nonplanar dust-ion-acoustic double layers in a dusty nonthermal plasma,

The solitary wave structures of the ion-acoustic waves propagating obliquely to an external uniform magnetic field have been considered in a low beta plasma consisting of warm adiabatic ions, nonthermal electrons, due to Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)], which generates the fast energetic electrons and electrons having a vortexlike distribution, due to Schamel [Plasma Phys. 13, 491 (1971); 14, 905 (1972)], taking care of both free and trapped electrons, immersed in a uniform static magnetic field. The nonlinear dynamics of ion-acoustic waves in such a plasma is shown to be governed by Schamel’s modified Korteweg–de Vries–Zakharov–Kuznetsov equation. When the coefficient of the nonlinear term of this equation vanishes, the vortexlike velocity distribution function of electrons simply becomes the isothermal velocity distribution function of electrons and the nonlinear behavior of the same ion-acoustic wave is described by a Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. A combined Schamel’s modified Korteweg–de Vries–Zakharov–Kuznetsov (S-KdV-ZK) equation is shown to describe the nonlinear behavior of ion-acoustic wave when the vortexlike velocity distribution function of electrons approaches the isothermal velocity distribution function of electrons, i.e., when the contribution of trapped electrons tends to zero. This combined S-KdV-ZK equation admits an alternative solitary wave solution having profile different from sech4 or sech2. The condition for the existence of this alternative solitary wave solution has been obtained. It is found that this alternative solitary wave solution approaches the solitary wave solution (sech2-profile) of the KdV-ZK equation when the contribution of trapped electrons tends to zero.

The criteria for the formation of envelope solitons and their basic features in a three-component degenerate relativistic quantum plasma (DRQP) system (containing relativistically degenerate electrons, non-degenerate inertial light nuclei, and stationary heavy nuclei) are theoretically investigated. The nonlinear Schrödinger equation is derived by employing the multi-scale perturbation technique. The envelope solitons are found to be associated with the modified ion-acoustic waves in which the inertia (restoring force) is provided by the mass density of light nuclei (degenerate pressure of cold electrons). The basic features of these envelope solitons, which are found to formed in such a DRQP system, and their modulational instability criteria (on the basis of the plasma parameters associated with the degenerate pressure of electrons, number densities of degenerate electrons, inertial light nuclei, and stationary heavy nuclei) are identified. The numerical simulations are also performed to confirm the stability of the envelope solitons predicted here by analytical analysis.