Effects of strength of dispersion and dust density on the formation of solitons and shocks in unmagnetized dusty plasma

The effects of strength of dispersion on the formation of solitons and shock waves in unmagnetized dusty plasma are studied using reductive perturbative technique. Different relational forms of the strength parameter e can be chosen to stretch the space and time variables, thereby leading to different types of nonlinearities. The Korteweg–de Vries (KdV) equation for the unmodulated dust acoustic wave is derived and the solitary wave solution is obtained. It is shown that there exists a critical dust density ndc at which the formation of the dust acoustic solitary waves is not possible. Furthermore, the solution of the KdV represents a rarefactive (compressive) solitary wave if nd ndc) where nd is the dust density. Using another type of coordinate transformation that reduces the strength of dispersion, the Burgers' equation with shock wave solution is obtained. Shocks with negative (positive) potentials are observed when nd ndc), respectively.

[1]  Abdullah Al Mamun.  Dust–electron-acoustic shock waves due to dust charge fluctuation , 2008 .

[2]  A. Sen,et al.  Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma. , 2008, Physical review letters.

[3]  Abdullah Al Mamun.  Effects of adiabaticity of electrons and ions on dust-ion-acoustic solitary waves , 2008 .

[4]  Mai-mai Lin,et al.  Dust acoustic solitary waves in a dusty plasmas with nonthermal ions , 2007 .

[5]  W. Moslem,et al.  Dust–ion–acoustic solitons and shocks in dusty plasmas , 2006 .

[6]  Gregor E. Morfill,et al.  Complex (dusty) plasmas: current status, open issues, perspectives , 2005 .

[7]  P. Shukla,et al.  Oblique Amplitude Modulation of Dust-Acoustic Plasma Waves , 2004, physics/0402049.

[8]  Abdullah Al Mamun,et al.  Solitons, shocks and vortices in dusty plasmas , 2003 .

[9]  D. Mendis.  Progress in the study of dusty plasmas , 2002 .

[10]  P. Shukla.  Dynamics of nonlinear dust lattice waves in the presence of ion plasma waves , 2002 .

[11]  Abdullah Al Mamun,et al.  Cylindrical and spherical dust ion–acoustic solitary waves , 2002 .

[12]  Abdullah Al Mamun,et al.  Introduction to Dusty Plasma Physics , 2001 .

[13]  P. Shukla.  A survey of dusty plasma physics , 2001 .

[14]  Abdullah Al Mamun.  Rarefactive ion-acoustic electrostatic solitary structures in nonthermal plasmas , 2000 .

[15]  R. Bingham,et al.  Shock waves in charge-varying dusty plasmas and the effect of electromagnetic radiation , 2000 .

[16]  D. Tskhakaya,et al.  LINEAR AND NONLINEAR DUST LATTICE WAVES IN PLASMA CRYSTALS , 1999 .

[17]  R. Merlino,et al.  Laboratory studies of waves and instabilities in dusty plasmas , 1998 .

[18]  C. B. Dwivedi,et al.  A new mathematical approach for shock-wave solution in a dusty plasma , 1997 .

[19]  Gabor J. Kalman,et al.  Dust acoustic waves in strongly coupled dusty plasmas , 1997 .

[20]  F. Melandsø.  Lattice waves in dust plasma crystals , 1996 .

[21]  R. Merlino,et al.  Experiments on ion-acoustic waves in dusty plasmas , 1996 .

[22]  R. Merlino,et al.  Laboratory observation of the dust-acoustic wave mode , 1995 .

[23]  Pandey,et al.  Self-consistent charge dynamics and collective modes in a dusty plasma. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  S. Vladimirov.  Propagation of waves in dusty plasmas with variable charges on dust particles , 1994 .

[25]  Vladimirov.  Amplification of electromagnetic waves in dusty nonstationary plasmas. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Sen,et al.  Collective effects due to charge-fluctuation dynamics in a dusty plasma. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  Varma,et al.  Electrostatic oscillations in the presence of grain-charge perturbations in dusty plasmas. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  P. Shukla,et al.  Large amplitude ion-acoustic solitons in a dusty plasma , 1992 .

[29]  P. Shukla,et al.  Dust ion-acoustic wave , 1992 .

[30]  L. Stenflo,et al.  Stimulated scattering of electromagnetic waves in dusty plasmas , 1992 .

[31]  N. N. Rao,et al.  DUST -ACOUSTIC WAVES IN DUSTY PLASMAS , 1990 .

[32]  V. Formisano,et al.  Ion plasma waves in dusty plasmas: Halley's comet , 1988, Journal of Plasma Physics.