  We show that the complex modified KdV (cmKdV) equation and generalized
nonlinear Schr\"odinger (GNLS) equation belong to the Ablowitz, Kaup, Newell
and Segur or so-called AKNS hierarchy. Both equations do not follow from the
action principle and are nonintegrable. By introducing some auxiliary fields we
obtain the variational principle for them and study their canonical structures.
We make use of a coupled amplitude-phase method to solve the equations
analytically and derive conditions under which they can support bright and dark
solitary wave solutions.
