Shallow water hydrodynamics Comparing solutions of the coupled Boussinesq equations in shallow water

There are several mathematical techniques to obtain the exact solutions of nonlinear Boussinesq equations. Commonly used techniques are: the homogeneous balance method, the G′/G-expansion method, the exp-function method, the Riccati equation approach, the variational iteration method, Fan’s F-expansion method, Lie symmetry method, sine-cosine method, Hirota bilinear transformation method. A commonality of all these methods is that when solving the solutions of nonlinear Boussinesq-like equations, they all must need the help of a computer algebra system, such as Maple or Mathematica.