The generalized Riccati equation mapping is extended with the basic G′/G -expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the 2 1 -dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equation G′ η w uG η...

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlin...

We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global pathwise uniqueness and the existence of pathwise solutions. New methods are employed to deal with a special type of boundary conditions and to verify the pathwise...

The Zakharov-Kuznetsov equation in spatial dimension $d\geq 5$ is considered. Cauchy problem shown to be globally well-posed for small initial data critical spaces and it proved that solutions scatter free as $t \to \pm \infty$. proof based on i) novel endpoint non-isotropic Strichartz estimates which are derived from the $(d-1)$-dimensional Schr\"odinger equation, ii) transversal bilinear rest...

In this paper we study the initial-value problem associated with dispersion generalized-Benjamin-Ono-Zakharov-Kuznetsov equation,ut+Dxa+1∂xu+uxyy+uux=0,a∈(0,1). More specifically, persistence property of solution in weighted anisotropic Sobolev spacesH(1+a)s,2s(R2)∩L2((x2r1+y2r2)dxdy), for appropriate s, r1 and r2. By establishing unique continuation properties also show that our results are sh...

This paper is concerned with the Cauchy problem of $2$D Zakharov-Kuznetsov equation. We prove bilinear estimates which imply local in time well-posedness Sobolev space $H^s({\mathbb{R}}^2)$ for $s > -1/4$, and these are optimal up to endpoint. utilize nonlinear version classical Loomis-Whitney inequality develop an almost orthogonal decomposition set resonant frequencies. As a corollary, we obt...