Linear and nonlinear analysis of dust acoustic waves in dissipative space dusty plasmas with trapped ions
الموضوعات : Journal of Theoretical and Applied Physics
A. M. El-Hanbaly
1
(Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University)
E. K. El-Shewy
2
(Department of Physics, Taibah University)
M. Sallah
3
(Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University)
H. F. Darweesh
4
(Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University)
الکلمات المفتاحية: mKdV–Burgers equation, Solitary and shock waves, Reductive perturbation method, Bifurcations, Vortex, like ion distribution,
ملخص المقالة :
AbstractThe propagation of linear and nonlinear dust acoustic waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negative dust grains has been investigated. The Boltzmann distribution is suggested for electrons whereas vortex-like distribution for ions. In the linear analysis, the dispersion relation is obtained, and the dependence of damping rate of the waves on the carrier wave number kdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$k$$end{document}, the dust kinematic viscosity coefficient ηddocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$eta _{d}$$end{document} and the ratio of the ions to the electrons temperatures σidocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$sigma _{i}$$end{document} is discussed. In the nonlinear analysis, the modified Korteweg–de Vries–Burgers (mKdV–Burgers) equation is derived via the reductive perturbation method. Bifurcation analysis is discussed for non-dissipative system in the absence of Burgers term. In the case of dissipative system, the tangent hyperbolic method is used to solve mKdV–Burgers equation, and yield the shock wave solution. The obtained results may be helpful in better understanding of waves propagation in the astrophysical plasmas as well as in inertial confinement fusion laboratory plasmas.
