New Exact traveling wave solutions of the (2+1) dimensional Zakharov-Kuznetsov (ZK) equation

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 straightforward and concise, and it can be also applied to other nonlinear evolution equations. The nonlinear evolution equations have a wide array in application of many fields, which described the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamic, plasma physics, nonlinear optics, etc. The investigation of the exact traveling wave solutions of nonlinear partial differential equations plays an important role in the study of nonlinear physical phenomena, for example, the wave phenomena observed in fluid dynamics, elastic media, optical fibers, etc. Since the knowledge of closedform solutions of nonlinear evolution equations NEEs ̄ facilitates the testing of numerical solvers, and aids in the stability analysis. The ZK equation is another alternative version of nonlinear model describing two-dimensional modulation of a kdv soliton [1, 2]. If a magnetic field is