Stability analysis for two-dimensional ion-acoustic waves in quantum plasmas

The quantum hydrodynamic model is applied to two-dimensional ion-acoustic waves in quantum plasmas. The two-dimensional quantum hydrodynamic model is used to obtain a deformed Kortewegde Vries (dKdV) equation by reductive perturbation method. By using the solution of auxiliary ordinary equations, a extended direct algebraic method is described to construct the exact solutions for nonlinear quantum dKdV equation. The present results are describing the generation and evolution of such waves, their interactions, and their stability.

[1]  Aly R. Seadawy,et al.  Nonlinear Dispersive Instabilities in Kelvin?Helmholtz Magnetohydrodynamic Flows , 2003 .

[2]  A. Nayfeh.  Introduction To Perturbation Techniques , 1981 .

[3]  Cheong R. Choi,et al.  Ion-acoustic solitary waves in a relativistic plasma , 2007 .

[4]  Aly R. Seadawy,et al.  Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma , 2014, Comput. Math. Appl..

[5]  P. Markowich,et al.  Quantum hydrodynamics, Wigner transforms, the classical limit , 1997 .

[6]  M. V. Kuzelev,et al.  METHODOLOGICAL NOTES: On the quantum description of the linear kinetics of a collisionless plasma , 1999 .

[7]  F. Haas,et al.  Modified Zakharov equations for plasmas with a quantum correction , 2004, physics/0410251.

[8]  M. Wadati,et al.  Nonlinear quantum dust acoustic waves in nonuniform complex quantum dusty plasma , 2007 .

[9]  G. Iafrate,et al.  Quantum correction to the equation of state of an electron gas in a semiconductor. , 1989, Physical review. B, Condensed matter.

[10]  A. Biswas,et al.  Shock wave solutions to the Bogoyavlensky–Konopelchenko equation , 2014 .

[11]  Carl L. Gardner,et al.  The Quantum Hydrodynamic Model for Semiconductor Devices , 1994, SIAM J. Appl. Math..

[12]  Lin Yi,et al.  Analytical traveling wave and soliton solutions of the generalized nonautonomous nonlinear Schrödinger equation with an external potential , 2013 .

[13]  Christian A. Ringhofer,et al.  The Chapman-Enskog Expansion and the Quantum Hydrodynamic Model for Semiconductor Devices , 2000, VLSI Design.

[14]  Aly R. Seadawy,et al.  Nonlinear Dispersive Rayleigh–Taylor Instabilities in Magnetohydrodynamic Flows , 2001 .

[15]  Chi-Kun Lin,et al.  A REVIEW OF DISPERSIVE LIMITS OF (NON)LINEAR SCHR¨ODINGER-TYPE EQUATIONS , 2000 .

[16]  P. Shukla,et al.  Dust acoustic solitary waves in a quantum plasma , 2006 .

[17]  Aly R. Seadawy,et al.  Traveling wave solutions for some coupled nonlinear evolution equations , 2013, Math. Comput. Model..

[18]  Ronald C. Davidson,et al.  Methods in Nonlinear Plasma Theory , 1973 .

[19]  A. H. Khater,et al.  General Soliton Solutions of an n-Dimensional Complex Ginzburg–Landau Equation , 2000 .

[20]  D. K. Choudhury,et al.  Approximate analytic solutions of spin dependent coupled Altarelli–Parisi equations using method of successive iteration , 2012 .

[21]  Aly R. Seadawy,et al.  Exact solutions of a two-dimensional nonlinear Schrödinger equation , 2012, Appl. Math. Lett..

[22]  Aly R. Seadawy,et al.  Variational method for the nonlinear dynamics of an elliptic magnetic stagnation line , 2006 .

[23]  F. Haas,et al.  Quantum ion-acoustic waves , 2003 .

[24]  Aly R. Seadawy,et al.  New exact solutions for the KdV equation with higher order nonlinearity by using the variational method , 2011, Comput. Math. Appl..