  When the Euler equations for shallow water are taken to the next order,
beyond KdV, momentum and energy are no longer exact invariants. (The only one
is mass.) However, adiabatic invariants (AI) can be found. When the KdV
expansion parameters are zero, exact invariants are recovered. Existence of
adiabatic invariants results from general theory of near-identity
transformations (NIT) which allow us to transform higher order nonintegrable
equations to asymptotically equivalent (when small parameters tend to zero)
integrable form. Here we present the direct method of calculations of adiabatic
invariants. It does not need a transformation to a moving reference frame nor
performing a near-identity transformation. Numerical tests show that deviations
of AI from almost constant values are indeed small.
