Abstract
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.
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