Abstract
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 solutions. The structures of the obtained solutions are distinct and stable.
Highlights
Many nonlinear evolution equations are playing important role in the analysis of some phenomena
The ZK equation governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field [4, 5]
In case [uy = Vy = 0], this system reduces to the set of coupled Korteweg-de Vries (KdV) equations
Summary
Many nonlinear evolution equations are playing important role in the analysis of some phenomena. A unified method, called the extended mapping method, is developed to obtain exact traveling wave solutions for a large variety of nonlinear partial differential equations [1, 2]. By means of this method, the solitary wave, the periodic wave, and the kink wave solutions can be obtained simultaneously. The application of DTM is successfully extended to obtain analytical approximate solutions to various linear and nonlinear problems [16, 17].
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