Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma

The Zakharov-Kuznetsov (ZK) equation is an isotropic nonlinear evolution equation, first derived for weakly nonlinear ion-acoustic waves in a strongly magnetized lossless plasma in two dimensions. In the present study, by applying the extended direct algebraic method, we found the electric field potential, electric field and magnetic field in the form of traveling wave solutions for the two-dimensional ZK equation. The solutions for the ZK equation are obtained precisely and the efficiency of the method can be demonstrated. The stability of these solutions and the movement role of the waves are analyzed by making graphs of the exact solutions.

[1]  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..

[2]  Fadi Awawdeh,et al.  New exact solitary wave solutions of the Zakharov-Kuznetsov equation in the electron-positron-ion plasmas , 2012, Appl. Math. Comput..

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

[4]  H. Shah,et al.  Nonlinear Zakharov–Kuznetsov equation for obliquely propagating two-dimensional ion-acoustic solitary waves in a relativistic, rotating magnetized electron-positron-ion plasma , 2005 .

[5]  Anjan Biswas,et al.  Solitary wave solution of the Zakharov–Kuznetsov equation in plasmas with power law nonlinearity , 2010 .

[6]  Ji-Huan He.  Application of homotopy perturbation method to nonlinear wave equations , 2005 .

[7]  Chang Lin,et al.  The formally variable separation approach for the modified Zakharov–Kuznetsov equation , 2007 .

[8]  Qing Xiao,et al.  New exact solitary wave and multiple soliton solutions of quantum Zakharov-Kuznetsov equation , 2010, Appl. Math. Comput..

[9]  Roger H.J. Grimshaw,et al.  Oblique Interactions between Internal Solitary Waves , 1994 .

[10]  E. Infeld,et al.  Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas. Part 2. Numerical simulations, two-soliton collisions , 1987 .

[11]  Yannis Kourakis,et al.  Nonlinear Dynamics of Rotating Multi-Component Pair Plasmas and e-p-i Plasmas , 2009 .

[12]  Bo Tian,et al.  Soliton solutions and interactions of the Zakharov-Kuznetsov equation in the electron-positron-ion plasmas , 2011 .

[13]  Cheng Zhang,et al.  Multisoliton solutions in terms of double Wronskian determinant for a generalized variable-coefficient nonlinear Schrödinger equation from plasma physics, arterial mechanics, fluid dynamics and optical communications , 2008 .

[14]  B. Kadomtsev,et al.  On the Stability of Solitary Waves in Weakly Dispersing Media , 1970 .

[15]  Aly R. Seadawy,et al.  The Solutions of the Boussinesq and Generalized Fifth-Order KdV Equations by Using the Direct Algebraic Method , 2012 .

[16]  Anup Bandyopadhyay,et al.  Existence and stability of alternative ion-acoustic solitary wave solution of the combined MKdV-KdV-ZK equation in a magnetized nonthermal plasma consisting of warm adiabatic ions , 2007 .

[17]  Bo Tian,et al.  Analytical study of the nonlinear Schrödinger equation with an arbitrary linear time-dependent potential in quasi-one-dimensional Bose–Einstein condensates , 2008 .