  In this work an extended elliptic function method is proposed and applied to
the generalized shallow water wave equation. We systematically investigate to
classify new exact travelling wave solutions expressible in terms of
quasi-periodic elliptic integral function and doubly-periodic Jacobian elliptic
functions. The derived new solutions include rational, periodic, singular and
solitary wave solutions. An interesting comparison with the canonical procedure
is provided. In some cases the obtained elliptic solution has singularity at
certain region in the whole space. For such solutions we have computed the
effective region where the obtained solution is free from such a singularity.
