in this paper, the convergence of zakharov-kuznetsov (zk) equation by homo- topy analysis method (ham) is investigated. a theorem is proved to guarantee the conver- gence of ham and to nd the series solution of this equation via a reliable algorithm.

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 find the series solution of this equation via a reliable algorithm. c ⃝ 2014 IAUCTB. All rights reserved.

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

In this paper, we study a generalized Zakharov–Kuznetsov equation in three variables, which has applications in the nonlinear development of ion-acoustic waves in a magnetized plasma. Conservation laws for this equation are constructed for the first time by using the new conservation theorem of Ibragimov. Furthermore, new exact solutions are obtained by employing the Lie symmetry method along w...

In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...

We present a general result of transverse nonlinear instability of 1-d solitary waves for Hamiltonian PDE’s for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1d model and the transverse perturbation “have the same sign”. Our result applies to the generalized KP-I equation, the Nonlinear Schrödinger equation, the generalized Bo...

We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation ∂tu+∆∂xu+u∂xu = 0 in the Sobolev spaces Hs(R3), s > 1, as well as in the Besov space B 2 (R 3). The proof is based on a sharp maximal function estimate in time-weighted spaces.

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the Padé technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger’s equation, compacton k(n, n) equation, Zakharov–Kuznetsov Zk(n, n) equation, and KdV and mKdV equations are given to show the effectiveness of the coupled VIM–Laplace–Pa...

In this article, we study and investigate the analytical solutions of space-time nonlinear fractional modified KDV-Zakharov-Kuznetsov (mKDV-ZK) equation. We have got new exact mKDV-ZK equation by using first integral method; found types hyperbolic trigonometric symbolic computation.