New (G′ / G) -Expansion Method and Its Applications to Nonlinear PDE

In this paper, the new (G′ / G)-expansion method is proposed for constructing more general exact solutions of nonlinear evolution equation with the aid of symbolic computation.By using this method many new and more general exact solutions have been obtained.To illus- trate the novelty and advantage of the proposed method, we solve the Zakharov-Kuznetsov- Benjamin-Bona-Mahony (ZKBBM) equation. Abundant exact travelling wave solutions of these equations are obtained, which include the exponential function solutions, the hyper- bolic function solutions and the trigonometric function solutions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.