  It is shown how the the introduction of a suitably defined dilatonic
auxiliary field, $\Phi$ say, makes it possible for the non-linear Lagrangian
for a generic elastic string model, of the kind appropriate for representing
superconducting cosmic strings, to be converted into a standardised form as the
sum of a kinetic term that is just homogeneously quadratic in the relevant
scalar phase gradient (as in a simple linear model) together with a potential
energy term, $V$ say, that is specified as a generically non-linear function of
$\Phi$. The explicit form of this function is derived for various noteworthy
examples, of which the most memorable is that of the transonic string model, as
characterised by a given mass scale, $m$ say, for which this potential energy
density will be expressible in terms of the zero current limit value
$\Phi_{_0}$ of $\Phi$ by $ V= {1\over 2} m \big(\Phi_{_0}^{-2} \Phi^2+
\Phi_{_0}^{2} \Phi^{-2} \big)$.
