Soliton solutions and modulation instability analysis of the coupled Zakharov-Kuznetsov equation

. The bright, dark and kink soliton solutions of the coupled Zakharov-Kuznetsov (ZK) equation are obtained by using the solitary wave ansatz method, variational approximation (VA), variational iteration method (VIM) and Adomian's decomposition method (ADM). The bright and dark soliton solutions are multiple soliton solutions at time t = 0 which reduce into stationary soliton through single soliton for sufficiently large time t . The approximate solutions by the VA, VIM and ADM are compared with the exact solution obtained by the ansatz method. The VIM gives better approximate solution of the coupled ZK equation than the VA. The absolute error and convergence analysis of the approximate solutions by the VIM and ADM show that the approximate solutions converge to the exact solution. The modulation instability is used to discuss the stability of the steady state solution of the coupled ZK equation and it demonstrates that the nonlinear term in the equation decides the modulational stability of the soliton solution.