In this article we study the smoothness properties of solutions to a two-dimensional coupled Zakharov-Kuznetsov system. We show that equations dispersive nature leads gain in regularity for solution. particular, if initial data (u0,v0) possesses certain and sufficient decay as x → ∞, then solution (u(t),v(t)) will be smoother than (u0, v0) 0 < t ≤ T where is existence time

We present a detailed numerical study of solutions to the (generalized) Zakharov–Kuznetsov equation in two spatial dimensions with various power nonlinearities. In $$L^{2}$$ -subcritical case, evidence is presented for stability solitons and soliton resolution generic initial data. $$L^2$$ -critical supercritical cases, appear be unstable against both dispersion blow-up. It conjectured that blo...

This paper studies the generalized version of theZakharov-Kuznetsov Benjamin-Bona-Mahoney equation. The functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. There are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. The results of this pape...

The repeated homogeneous balance method is used to construct new exact traveling wave solutions of the (2+1) dimensional ZakharovKuznetsov (ZK) equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions are successfully obtained. This method is straight...

Propagation of dust acoustic waves (DAWs) with the effect of power law dust size distribution (DSD) in a magnetized dusty plasma with opposite polarity dust is studied. Using a reductive perturbation method, a Zakharov-Kuznetsov equation appropriate for describing three-dimensional DAWs is derived. The compressive and rarefactive solitons are possible in the present model. Due to the DSD effect...

We consider the focusing modified Zakharov–Kuznetsov (mZK) equation in two space dimensions. prove that solutions which blow up finite time \(H^1(\mathbb {R}^{2})\) norm have property they concentrate a non-trivial portion of their mass (more precisely, at least amount equal to ground state) blow-up time. For finite-time \(H^s(\mathbb {R}^2)\) for \(\frac{17}{18}< s < 1\), we slightly weaker re...

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solution...

This paper studies the generalized version of the ZakharovKuznetsov Benjamin-Bona-Mahoney equation. The functional variable method as well as the simplest equation method are applied to obtain solitons and singular periodic solutions to the equation. There are several constraint conditions that are naturally revealed in order for these specialized type of solutions to exist. The results of this...