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

Evolution equations for pulse propagation in nonlinear media