By means of two extended (G0
/G)-expansion methods, new approach of (G0
/G)-expansion
method and new approach of generalized (G0
/G)-expansion method, we have successfully performed
for analytical solutions on the Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation. In methods, the nonlinear auxiliary equation is implemented for constructing a rich class of
new travelling wave solutions. Moreover, obtained solutions reveal that, these methods are very
effective and powerful to handle various nonlinear evolution equations which frequently arise in
mathematical physics, engineering sciences and many scientific real time application fields.