This paper studies the generalized (2 + 1)-dimensional Zakharov-Kuznetsov Equation using the (G'/G)-expand method, we obtain many new explicit solutions of the generalized (2 + 1)-dimensional Zakharov-Kuznetsov Equation, which include hyperbolic function solutions, trigonometric function solutions and rational function solutions and so on.

We derive the Zakharov-Kuznetsov equation for large scale motion from the barotropic quasigeostrophic equation in a weakly nonlinear, long wave approximation. We study the evolution of finite amplitude perturbations of an unstable jet in planetary atmospheres and oceans. We use multiple scale analysis combined with asymptotic matching. The Zakharov-Kuznetsov equation is suggestive that the pert...

In this paper, the convergence of Zakharov-Kuznetsov (ZK) equation by homotopy analysis method (HAM) is investigated. A theorem is proved to guarantee the convergence of HAM and to nd the series solution of this equation via a reliable algorithm.

The evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation, which describes mass transport along the surface of nanoconductors, is studied. Approximate equations are developed for these equations, these approximate equations including the important effect of the dispersive radiation shed by the lumps as they evolve. The approximate equations sh...

In this paper, we investigate the instability of one-dimensionally stable periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Zakharov-Kuznetsov equation in two space dimensions. By deriving appropriate asymptotic expansions of the periodic Evans function, we derive an index which yields sufficient condit...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

The aim of this paper is by using the fractional complex transform and the optimal homotopy analysis by method (OHAM) to find the analytical approximate solutions for nonlinear partial fractional differential Zakharov-Kuznetsov equation. Fractional complex transformation is proposed to convert nonlinear partial fractional differential Zakharov-Kuznetsov equation to nonlinear partial differentia...

We consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation ut + 6uux + uxxx + uxyy = 0, (x, y) ∈ R, t ∈ R, which is known to have global solution for given data in u(x, y, 0) = u0(x, y) ∈ H(R) satisfying ‖u0‖L2 < √ 3‖φ‖L2 , where φ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakhar...

Exact solutions to conformable time fractional (3+1)dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE. The resultant polynomial equation is solved by using algebrai...