Construction of solitary wave solutions of some nonlinear dynamical system arising in nonlinear water wave models
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ORIGINAL PAPER
Construction of solitary wave solutions of some nonlinear dynamical system arising in nonlinear water wave models A R Seadawy1*, D Lu2 and N Nasreen2 1
Mathematics Department, Faculty of Science, Taibah University, Medina, Saudi Arabia
2
Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, People’s Republic of China Received: 14 April 2019 / Accepted: 23 July 2019
Abstract: The higher order of nonlinear partial differential equations in mathematical physics is studied. We used the analytical mathematical methods of the nonlinear (3?1)-dimensional extended Zakharov–Kuznetsov dynamical, modified KdV–Zakharov–Kuznetsov and generalized shallow water wave equations to demonstrate the efficiency and validity of the proposed powerful technique. The shallow water wave models have been applied in tidal waves and weather simulation. Exact wave solutions of these models in various forms such as Kink and anti-Kink solitons, bright–dark soliton, solitary wave and periodic solutions are constructed that have plenty of applications in diverse areas of physics. Graphically, we presented the movement of some obtained solitary wave solutions that aids in understanding the physical phenomena of these models. Keywords: Extended Zakharov–Kuznetsov dynamical model; Modified KdV–Zakharov–Kuznetsov model; Generalized (3?1) shallow water; Solitons; Solitary wave solutions PACS Nos.: 02.30.Jr; 05.45.Yv; 47.10.A; 47.35.?i; 47.35.Fg
1. Introduction The generalized KdV Zakharov–Kuznetsov (ZK) models are significant for various physical phenomena such as waves in nonlinear resonant circuit, stratified internal and shallow water wave, waves of ion acoustic in plasma physics, astrophysics and space environment, nonlinear optic, hydrodynamic and many more [1–6]. Furthermore, the static solitary waves have been found in different areas, for example solar, wind, polar magnetosphere and magnetotail [2], etc. In nonlinear phenomena, solitons and solitary waves show motivating and famous properties which have many significant features, especially in extended equations. The ZK models are one of the two wellexamined canonical two-dimensional modifications of KdV model [7]. In quantum magneto-plasmas [8–10], nonlinear extended Zakharov–Kuznetsov (E–ZK) equations are used to examine the propagation of nonlinear dust waves of ion
acoustic in magnetized temperature of two-ion-dusty plasma and small frequency ion acoustic wave. By utilizing the concept of reductive perturbation, the researcher in [11] derived a nonlinear three-dimensional E–ZK model. The modified KdV (mKdV) equation can be derived for the expansion of ion acoustic perturbation in plasma with component of two negative ions of diverse temperature [12]. The modified KdV-ZK model occurs in the weakly condition of two-dimensional variation in the mKdV equation [12], which plays an important role in dissimilar branches of physics and mathematical physics to inspect major features of nonlinear promulgation of different physical phenomenal systems [13–25]. The shal
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