Exact solutions of shallow water wave equations by using the -expansion method

In this work, we establish exact solutions for (2 + 1)- and (3 + 1)-dimensional shallow water wave equations. The -expansion method is used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed in terms of hyperbolic functions, trigonometric functions and rational functions. This method presents a wider applicability for handling nonlinear wave equations.