Exact travelling wave solutions of nonlinear evolution equations in (1+1) and (2+1) dimensions

Based upon the symbolic computation system Maple, the projective Riccati equation method is improved to seek for travelling wave solutions in (1+1) and (2+1)-dimensional nonlinear evolution equations by introducing two new elementary bell-shaped and kink-shaped functions. The validity and reliability of the method is tested by applying it to the (2+1)-dimensional generalized of the shallow water wave equation, potential KdV equation and Burgers-KdV equation.