Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries （vcKdV） model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by th...Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries （vcKdV） model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by the Hirota method and Wronskian technique. Additionally, the bilinear auto-Bǎcklund transformation between （N-1）- soliton-like and N-soliton-like solutions is verified.展开更多
The nonlinear propagation of waves (specially solitary waves) in an ultra-relativistic degenerate dense plasma (containing ultra-relativistic degenerate electrons and positrons, cold, mobile, inertial ions, and negati...The nonlinear propagation of waves (specially solitary waves) in an ultra-relativistic degenerate dense plasma (containing ultra-relativistic degenerate electrons and positrons, cold, mobile, inertial ions, and negatively charged static dust) have been investigated by the reductive perturbation method. The linear dispersion relation and Korteweg de-Vries equation have been derived whose numerical solutions have been analyzed to identify the basic features of electrostatic solitary structures that may form in such a degenerate dense plasma. The existence of solitary structures has been also verified by employing the pseudo-potential method. The implications of our results in astrophysical compact objects have been briefly discussed.展开更多
Nonlinear propagation of dust-ion-acoustic waves in a degenerate dense plasma (with the constituents being degenerate, for both the limits non-relativistic or ultra-relativistic) have been investigated by the reductiv...Nonlinear propagation of dust-ion-acoustic waves in a degenerate dense plasma (with the constituents being degenerate, for both the limits non-relativistic or ultra-relativistic) have been investigated by the reductive perturbation method. The Korteweg de-Vries (K-dV) equation and Burger’s equation have been derived, and the numerical solutions of those equations have been analyzed to identify the basic features of electrostatic solitary and shock structures that may form in such a degenerate dense plasma. The implications of our results in compact astrophysical objects, particularly, in white dwarfs, have been briefly discussed.展开更多
The one-dimensional quantum hydrodynamic (QHD) model for a three-specie quantum plasma is used to study the quantum counterpart of the well known dust ion-acoustic wave (DIAW). It is found that owing to the quantum ef...The one-dimensional quantum hydrodynamic (QHD) model for a three-specie quantum plasma is used to study the quantum counterpart of the well known dust ion-acoustic wave (DIAW). It is found that owing to the quantum effects, the dynamics of small but finite amplitude quantum dust ion-acoustic waves (QDIA) is governed by a deformed Korteweg-de Vries equation (dK-dV). The latter admits compressive as well as rarefactive stationary QDIA solitary wave solution. In the fully quantum case, the QDIA soliton experiences a spreading which becomes more significant as electron depletion is enhanced.展开更多
The prominent features of higher order nonlinear ion-acoustic waves involving quantum corrections in an unmagnetized quantum dusty plasma are revisited with the theoretical framework of Hossain et al. [1]. The fluid m...The prominent features of higher order nonlinear ion-acoustic waves involving quantum corrections in an unmagnetized quantum dusty plasma are revisited with the theoretical framework of Hossain et al. [1]. The fluid model is demonstrated here by its constituent inertial ions, Fermi electrons with quantum effect, and immovable dust grain with negative charge. We have used the ideology of Gardner equation. The well-known RPM method is employed to derive the equation. Indeed, the basic features of quantum dust ion-acoustic Gardner solitons (GSs) are pronounced here. GSs are shown to exist for the value of dust to ion ratio around 2/3 which is valid for space plasma [2], and are different from those of K-dV (Korteweg-de Vries) solitons, which do not exist for the value around 2/3. The implications of our results are suitable for cosmological and astrophysical environments.展开更多
基金Supported by the Key Project of the Ministry of Education of China under Grant No 106033, and the National Natural Science Foundation of China under Grant Nos 60372095 and 10272017, the Green Path Programme of Air Force of the Chinese People＇s Liberation Army, the Cheung Kong Scholars Programme of the Ministry of Education of China, and Li Ka Shing Foundation of Hong Kong.
文摘Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries （vcKdV） model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by the Hirota method and Wronskian technique. Additionally, the bilinear auto-Bǎcklund transformation between （N-1）- soliton-like and N-soliton-like solutions is verified.
文摘The nonlinear propagation of waves (specially solitary waves) in an ultra-relativistic degenerate dense plasma (containing ultra-relativistic degenerate electrons and positrons, cold, mobile, inertial ions, and negatively charged static dust) have been investigated by the reductive perturbation method. The linear dispersion relation and Korteweg de-Vries equation have been derived whose numerical solutions have been analyzed to identify the basic features of electrostatic solitary structures that may form in such a degenerate dense plasma. The existence of solitary structures has been also verified by employing the pseudo-potential method. The implications of our results in astrophysical compact objects have been briefly discussed.
文摘Nonlinear propagation of dust-ion-acoustic waves in a degenerate dense plasma (with the constituents being degenerate, for both the limits non-relativistic or ultra-relativistic) have been investigated by the reductive perturbation method. The Korteweg de-Vries (K-dV) equation and Burger’s equation have been derived, and the numerical solutions of those equations have been analyzed to identify the basic features of electrostatic solitary and shock structures that may form in such a degenerate dense plasma. The implications of our results in compact astrophysical objects, particularly, in white dwarfs, have been briefly discussed.
文摘The one-dimensional quantum hydrodynamic (QHD) model for a three-specie quantum plasma is used to study the quantum counterpart of the well known dust ion-acoustic wave (DIAW). It is found that owing to the quantum effects, the dynamics of small but finite amplitude quantum dust ion-acoustic waves (QDIA) is governed by a deformed Korteweg-de Vries equation (dK-dV). The latter admits compressive as well as rarefactive stationary QDIA solitary wave solution. In the fully quantum case, the QDIA soliton experiences a spreading which becomes more significant as electron depletion is enhanced.
文摘The prominent features of higher order nonlinear ion-acoustic waves involving quantum corrections in an unmagnetized quantum dusty plasma are revisited with the theoretical framework of Hossain et al. [1]. The fluid model is demonstrated here by its constituent inertial ions, Fermi electrons with quantum effect, and immovable dust grain with negative charge. We have used the ideology of Gardner equation. The well-known RPM method is employed to derive the equation. Indeed, the basic features of quantum dust ion-acoustic Gardner solitons (GSs) are pronounced here. GSs are shown to exist for the value of dust to ion ratio around 2/3 which is valid for space plasma [2], and are different from those of K-dV (Korteweg-de Vries) solitons, which do not exist for the value around 2/3. The implications of our results are suitable for cosmological and astrophysical environments.
