Head-on collision of dust acoustic shock waves in quantum plasma

Abstract

An investigation is presented to study head-on collision of two dust acoustic (DA) shock waves in quantum dusty plasma comprising negative dust, electrons, and ions. Using an extended Poincare-Lighthill-Kuo perturbation method, two Kortweg-de Vries-Burgers equations for shock waves are derived in this plasma. The analytical phase shifts of DA shock waves after collision has been deduced. The effect of various physical parameters such as quantum diffraction, quantum statistics, kinematic viscosity, and temperature ratio on the characteristics of DA shock waves is explored. This study may be of relevance in astrophysical plasmas such as neutron stars and white dwarfs.

Numerical solution and characteristic study of time-fractional shocks collision

“…It is assumed that locations of IA shock waves Φ 2ξ (Φ 2η ) are η → + L (ξ → − L) before collision and η → − L (ξ → + L) after collision where L ? 1 but L ≠ ∞ [14,24]. Consequently, we get the following corresponding phase shift of the right and left IA shock waves.…”

“…We assumed small amplitude ion acoustic shocks so that the counter traveling shocks interact quasi elastically. To analyze shocks waves interaction by following the extended PLK method in the cited literature [65,66], the stretching of independent variables (space and time coordinates) are introduced as [67]…”

“…In quantum dusty plasma, which consists of negative dust, electrons and ions, the author Kohli et. al., [24] reported collision of the two counter traveling DA shock waves. They studied the effects of kinematic viscosity, temperature ratio and quantum diffraction on the characteristics of DA shock waves.…”

Boundary effects on dispersion relations of ion-acoustic wave and physical properties of overlapping soliton in a plasma waveguide

“…We employ the Poincaré-Lighthill-Kuo (PLK) perturbation method to generate two interacting solitons and obtain the expression of the overlapping soliton. Motivated by the pioneering work by Su and Mirie [36], a considerable amount of work [37][38][39][40][41][42][43][44][45][46][47][48][49] has been done related to the interaction between solitons in different plasma systems. According to this method, stretched space and time coordinates with phase functions, given by where v is the phase speed of colliding solitons, ξ (η) and r A (r B ) represent the propagation trajectory and initial position of the outward (inward) traveling soliton, respectively.…”

“…Substituting equations ( 43) and (44)into equations (40)∼ (42), and by equating the powers of ò, one can obtain two sets of equations, the leading order gives…”