Abstract
This paper is devoted to improving the general Kudryashov method by a new and general auxiliary equation. So, a new method is introduced, which we call 'the general improved Kudryashov method', to produce exact solutions for nonlinear evolution equations arising in mathematical physics. As application examples, exact traveling wave solutions for the combined Korteweg-de Vries and modified Korteweg-de Vries (KdV-mKdV) equation and the (2+1)-dimensional Zakharov-Kuznetsov equation are obtained. These solutions can be classified as solitary and periodic wave solutions. Some of the obtained solutions are graphically sketched.