A variational method given by Ritz has been applied to the Zakharov equation to construct an analytical solution. The solution of Zakharov equation gives a good description of both linear and nonlinear evolutions of instabilities generated in waves due to modulation. The spatially periodic trial function is chosen in the form of combination of Jacobian elliptic functions with the dependence of ...

We prove low-regularity global well-posedness for the 1d Zakharov system and 3d Klein-Gordon-Schrödinger system, which are systems in two variables u : Rx × Rt → C and n : Rx × Rt → R. The Zakharov system is known to be locally well-posed in (u, n) ∈ L2×H−1/2 and the Klein-Gordon-Schrödinger system is known to be locally well-posed in (u, n) ∈ L × L. Here, we show that the Zakharov and Klein-Go...

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.

In this article the scattering matrix pertaining to the defocusing matrix Zakharov-Shabat system on the line is related to the scattering operator arising from time-dependent scattering theory. Further, the scattering data allowing for a unique retrieval of the potential in the defocusing matrix Zakharov-Shabat system are characterized. Mathematics Subject Classification (2000). Primary 34A55, ...

In this work, by using a simple transformation technique, we have show that the nonlinear wave equations: Zakharov equations and generalized Zakharov equations can be reduced to the same family of Duffing or double-well Duffing equations. Then by means of quotient trigonometric function expansion method, many kinds of exact and explicit solutions of this family of equations are obtained in a un...

In this paper, fractional complex transform (FCT) with help of variational iteration method (VIM) is used to obtain numerical and analytical solutions for the fractional Zakharov–Kuznetsov equations. Fractional complex transform (FCT) is proposed to convert fractional Zakharov– Kuznetsov equations to its differential partner and then applied VIM to the new obtained equations. Several examples a...

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.

Based on the extended hyperbolic functions method, we obtain the multiple exact explicit solutions of the Klein–Gordon–Zakharov equations. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for u and n, (b) the solitary wave solutions of kink-type for u and bell-type for n, (c) the solitary wave solutions of a compound of the bell-type and the kink-type fo...