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...