The new exact solitary and multi-soliton solutions for the (2+1)-dimensional Zakharov–Kuznetsov equation. (15th April 2018) - Kuo, Chun-Ku
Abstract: In this paper, by employing two different simplest equation methods, the (2 + 1)-dimensional Zakharov–Kuznetsov (ZK) equation derived for describing weakly nonlinear ion-acoustic waves in the plasma is investigated. With the aid of the Bernoulli equation and the coupled Burgers' equations, the electric field potential of ZK equation are formally obtained, which are presented as the new solitary and multi-soliton solutions. Meanwhile, the electric field and magnetic field can be accordingly obtained. In addition, the significant features of the variable coefficient and parameter are discovered. The results show that the solitary and multi-soliton solutions are precisely obtained and the efficiency of the methods is demonstrated. These new exact solutions will extend previous results and help to explain the features of nonlinear ion-acoustic waves in the plasma.