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...