  We consider equations in the modified KdV (mKdV) hierarchy and make use of
the Miura transformation to construct expressions for their Lax pair. We derive
a Lagrangian-based approach to study the bi-Hamiltonian structure of the mKdV
equations. We also show that the complex modified KdV (cmKdV) equation follows
from the action principle to have a Lagrangian representation. This
representation not only provides a basis to write the cmKdV equation in the
canonical form endowed with an appropriate Poisson structure but also help us
construct a semianalytical solution of it. The solution obtained by us may
serve as a useful guide for purely numerical routines which are currently being
used to solve the cmKdV eqution.
