  We prove the nonsqueezing property of the coupled Korteweg-de Vries (KdV)
equation. Relying on Gromov's nonsqueezing theorem for finite dimensional
Hamiltonian systems, the argument is to approximate the solutions to the
original infinite dimensional Hamiltonian system by a frequency truncated
finite dimensional system, and then the nonsqueezing property is transferred to
the infinite dimensional system. This is the argument used by Bourgain for the
1D cubic NLS flow, and Colliander et. al. for the KdV flow. One of main
ingredients of \cite{Colliander:2005vv} is to use the Miura transform to change
the KdV flow to mKdV flow. In this work, we consider the coupled KdV equations
for which the Miura transform is not available. Instead of the Miura transform,
we use the method of the normal form via the differentiation by parts. Although
we present the proof for the coupled KdV equation, the same proof is applicable
to the KdV flow, and so provide alternative simplified proof for the KdV flow.
