Content area
Full Text
Astrophys Space Sci (2013) 347:293298 DOI 10.1007/s10509-013-1529-8
O R I G I NA L A RT I C L E
Bifurcations of dust ion acoustic travelling waves in a magnetized quantum dusty plasma
Utpal Kumar Samanta Asit Saha Prasanta Chatterjee
Received: 13 March 2013 / Accepted: 3 June 2013 / Published online: 27 June 2013 Springer Science+Business Media Dordrecht 2013
Abstract Bifurcation behavior of nonlinear dust ion acoustic travelling waves in a magnetized quantum dusty plasma has been studied. Applying the reductive perturbation technique (RPT), we have derived a Kadomtsev-Petviashili (KP) equation for dust ion acoustic waves (DIAWs) in a magnetized quantum dusty plasma. By using the bifurcation theory of planar dynamical systems to the KP equation, we have proved that our model has solitary wave solutions and periodic travelling wave solutions. We have derived two exact explicit solutions of the above travelling waves depending on different parameters.
Keywords Quantum dusty plasma Bifurcation theory
Solitary wave Periodic wave
1 Introduction
The classical plasmas are characterized by low densities and high temperature where as quantum plasmas are constituted by high densities and low temperature. Recently a remarkable interest has been drawn on quantum effects in plasma due to its wide domain of applicability. These important effects are quantum plasma echo (Manfredi and Feix
U.K. SamantaDepartment of Mathematics, Bankura Christian College, Bankura 722101, West Bengal, India
A. Saha ( )
Department of Mathematics, Sikkim Manipal Institute of Technology, Majitar, Rangpo, East-Sikkim 737136, India e-mail: [email protected]
P. ChatterjeeDepartment of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan 731235, India
1996), quantum instabilities in Fermi gas (Manfredi and Haas 2001), quantum Landau damping (Suh et al. 1991), fabrication of semiconductor devices (Markowhich et al. 1990) quantum dots and quantum wires (Shpatakovskaya 2006) quantum wells, carbon nanotubes and quantum diodes (Ang et al. 2003, 2004; Shukla and Eliasson 2008). A several experiments have been carried out in dense plasma (particularly in astrophysical and cosmological studies) (Chabrier et al. 2002; Jung 2001), in dusty plasmas, in microelectronic devices (Markowhich et al. 1990), in nonlinear optics (Agrawal 1995) etc. to understand these effects on the behavior of linear and nonlinear wave propagations. Many authors have investigated quantum hydrodynamical model (QHD) to study the quantum effects. Obviously the QHD model is an extension of...