  Some modified (defocusing) non-linear Schr\"odinger models (MNLS) possess
infinite towers of anomalous conservation laws with asymptotically conserved
charges. The so-called anomalies of the quasi-conservation laws vanish upon
space-time integration for a special ${\cal C}{\cal P}_s{\cal T}_d$ symmetric
field configurations. We verify numerically the degree of modifications of the
charges around the dark-soliton interaction regions by computing numerically
some representative anomalies related to lowest order quasi-conservation laws
of the non-integrable cubic-quintic NLS model as a modified (defocusing) NLS
model. This modification depends on the parameter $\epsilon$, such that the
standard NLS is recovered for $\epsilon=0$. Here we present the numerical
simulations for small values of $|\epsilon|$, and show that the collision of
two dark solitons are elastic. The NLS-type equations are quite ubiquitous in
several areas of non-linear science.
