  In this Letter we study the evolution of the higher-order squeezing, namely,
$n$th-order single-mode squeezing, sum- and difference-squeezing for the
codirectional Kerr nonlinear coupler. We show that the amount of squeezing
decreases when $n$, i.e. the squeezing order, increases. For specific values of
the interaction parameters squeezing factors exhibit a series of
revival-collapse phenomena, which become more pronounced when the value of $n$
increases. Sum-squeezing can provide amounts of squeezing greater than those
produced by the $n$th higher-order ($n\geq 2$) squeezing for the same values of
interaction parameters and can map onto amplitude-squared squeezing. Further,
we prove that the difference-squeezing is not relevant measure for obtaining
information about squeezing from this device.
