The modied Zakharov–Kuznetsov (mZK) equation, ut + uux + uxxx + uxyy = 0, (1) represents an anisotropic two-dimensional generalization of the Korteweg–de Vries equation and can be derived in a magnetized plasma for small amplitude Alfvén waves at a critical angle to the undisturbed magnetic field, and has been studied by many authors because of its importance [1–5]. However, Eq. (1) possesses m...

The   ) ( exp    -expansion method is a promising method for finding exact traveling wave solutions to nonlinear evolution equations in physical sciences. In this article, we use the   ) ( exp    -expansion method to find the exact solutions for the nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation and the good Boussinesq equations. Many solitary wave solutions are formally d...

Local well-posedness for the two-dimensional Zakharov-Kuznetsov equation in fully periodic case with initial data Sobolev spaces $H^s$, $s>1$, is proved. Frequency dependent time localization utilized to control derivative nonlinearity. The new ingredient improve on previous results a nonlinear Loomis-Whitney-type inequality.

In this paper,the traditional G′/G-expansion method is improved and a generalized G′/G-expansion method is proposed to seek exact solutions of nonlinear evolution equations.And we choose Benjamin-Bona-Mahony equation,(2+1) dimensional generalized Zakharov-Kuznetsov equation and variant Bousinessq equations to illustrate the validity and advantages of the proposed method.It is shown that the pro...