Higher-order corrections to dust ion-acoustic soliton in a quantum dusty plasma

Abstract

Dust ion-acoustic soliton is studied in an electron-dust-ion plasma by employing a two-fluid quantum hydrodynamic model. Ions and electrons are assumed to follow quantum mechanical behaviors in dust background. The Korteweg–de Vries (KdV) equation and higher order contribution to KdV equations are derived using reductive perturbation technique. The higher order contribution is obtained as a higher order inhomogeneous differential equation. The nonsecular solution of the higher order contribution is obtained by using the renormalization method and the particular solution of the inhomogeneous equation is determined using a truncated series solution method. The effects of dust concentration, quantum parameter for ions and electrons, and soliton velocity on the amplitude and width of the dressed soliton are discussed.

Dust ion‐acoustic solitons collision in weakly relativistic plasmas with superthermality‐distributed electrons and positrons: Higher‐order phase shifts

“…In the next order (i.e., 1 ), substituting Equations (35) and (36) into Equations (29) and (30), respectively, we arrive at In the next order (i.e., 1 ), substituting Equations (35) and (36) into Equations (29) and (30), respectively, we arrive at…”

“…Combining Equations (35), (36), (40), (41), (43), and (44) into Equations (20), (21), (24), and (25), we obtain the solutions of the KdVEs with fifth-order dispersion terms. [30,32] where F 1 = (f 1 + f 2 1 + 2 f 3 ( 1 ) 2 ), F 2 = ( f 2 + 2 2 f 3 1 ), and F 3 = 2 f 3 ,…”

“…where 01,02 (=3 (0) 1,2 / A 1,2 ) and W 1,2 (= √ A 1,2 01,02 ∕12B) are the amplitudes and the widths of solitons. In the next order (i.e., 1 ), substituting Equations (35) and (36) into Equations (29) and (30), respectively, we arrive at L Φ (1) 11 = (3(A 1 01 ∕3) 3∕2 (− (1) 1 + (A 1 01 ∕3) 2 )sech 2 (W 1 1 ) + (A 1 01 ∕3) 7∕2 (−45sech 4 (W 1 1 ) + 67.5 sech 6 (W 1 1 ))) tanh(W 1 1 ),…”

“…High-energy particles (i.e., electrons and positrons) produced as a result of stochastic heating processes when the pulsar relativistic wind collides with the ejecta of supernova explosion surrounding the pulsar. [34,35] In other words, the KdVEs with fifth-order dispersion terms are applied and H-O solutions are obtained. Consequently, the dust particles are considered as immobile grains.…”

“…[30][31][32][33] Basically, this method depends on the H-O approximation of the reductive perturbation analysis. [34,35] In other words, the KdVEs with fifth-order dispersion terms are applied and H-O solutions are obtained. Consequently, the corresponding H-O phase shifts are presented.…”