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Chin. Phys. B, 2016, Vol. 25(10): 105202    DOI: 10.1088/1674-1056/25/10/105202

K—P—Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

A N Dev1, M K Deka2, J Sarma3, D Saikia4, N C Adhikary4
1 Department of Mathematics, Siksha ‘O' Anusandhan University, Khandagiri, Bhubaneswar-751030, Odisha, India;
2 Department of Applied Sciences, Institute of Science and Technology, Gauhati University, Guwahati 781014, Assam, India;
3 Department of Mathematics, R G Baruah College, Guwahati-781025, Assam, India;
4 Physical Sciences Division, Institute of Advanced Study in Science and Technology, Vigyan Path, Paschim Boragaon, Garchuk, Guwahati-781035, Assam, India
Abstract  The stationary solution is obtained for the K-P-Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev-Petviashvili (K-P) equation, three-dimensional (3D) Burgers equation, and K-P-Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave (DIASW). The K-P equation predictes the existences of stationary small amplitude solitary wave, whereas the K-P-Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.
Keywords:  K-P-Burgers equation      negative ion      relativistic plasma      reductive perturbation method     
Received:  23 January 2016      Published:  05 October 2016
PACS:  52.27.Lw (Dusty or complex plasmas; plasma crystals)  
  52.35.Fp (Electrostatic waves and oscillations (e.g., ion-acoustic waves))  
  52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))  
  52.35.Tc (Shock waves and discontinuities)  
Corresponding Authors:  N C Adhikary     E-mail:

Cite this article: 

A N Dev, M K Deka, J Sarma, D Saikia, N C Adhikary K—P—Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity 2016 Chin. Phys. B 25 105202

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