Modulated heavy nucleus-acoustic waves and associated rogue waves in a degenerate relativistic quantum plasma system

Abstract

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.

Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

“…For instance, it has been well established that they may appear in physical systems as the consequence of the interplay between nonlinear and dispersive effects, under the activation of the so-called MI phenomenon [3][4][5][6][7][8]. Recently, interest in studying RWs has gone beyond oceanography and hydrodynamics [9,10] to reach some other areas related to optics and photonics [11][12][13][14], Bose-Einstein condensation [15][16][17], biophysics [18][19][20][21], plasma physics [22,23], just to name a few. Particularly, ion-acoustic super-RWs were found in an ultra-cold neutral plasma in the presence of ion-fluid and nonextensive electron distribution [24].…”

“…Modulated IAWs appear in physical systems as the consequence of the interplay between nonlinearity and dispersion. Therefore, to explicitly include such effects, the RPM is commonly used [22,24,36,37], which results in equations describing the development of the modulation of the amplitude in the lowest order of an asymptotic expansion. To start, we introduce the stretched variables in space and time as = (x − v g t) and = 2 t , where the group velocity v g will be determined later by the solvability condition of Eq.…”

“…In hydrodynamics, it describes the interaction between short-wave and long-wave gravitational disturbances in the atmosphere [54][55][56]. Other applications appear in water waves at the free surface of an ideal fluid and in plasma physics (interaction between Langmuir and ionacoustic waves [22,23,27,36,42]). Applications of the NLS equation in fiber optics have stimulated further studies in optical communications [57][58][59][60].…”

Self‐gravito‐acoustic waves and their instabilities in a self‐gravitating degenerate quantum plasma system

“…The SGDQP system will be in equilibrium when this outward degenerate pressure of all the degenerate plasma species is counterbalanced by the inward poll of the same by the self-gravitational pressure. A large number of authors [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] have considered the degenerate plasma systems including/excluding the effect of self-gravitational field to study the electro/magneto-acoustic linear/nonlinear waves, but not to study any kind of self-gravito-acoustic (SGA) waves. white dwarfs, neutron stars, etc.…”

“…Once the SGDQP system is perturbed, new waves (which can be referred to as "degenerate pressure driven self-gravito-acoustic [DPDSGA] waves") are emitted because of its compression and rarefaction, and vice-versa. A large number of authors [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] have considered the degenerate plasma systems including/excluding the effect of self-gravitational field to study the electro/magneto-acoustic linear/nonlinear waves, but not to study any kind of self-gravito-acoustic (SGA) waves. Thus, in the present work, we investigate the DPDSGA waves to identify their dispersion properties and stable/unstable regimes depending on degenerate quantum plasma parameters.…”