Missing Terms in Weinberg's treatment of perturbations on Newtonian Cosmology

I was reading Appendix F of Steven Weingberg's book "Cosmology". In this Appendix he works out the perturbations to a cosmological fluid described by non-relativistic hydrodynamics and Newtonian gravity.

It turns out that the first order perturbations satisfy,

$$
frac{partial delta rho }{partial t } + 3 H delta rho + H vec{X} cdot nabla delta rho + bar{rho} nabla cdot vec{v} = 0, qquad tag{1}
$$

$$
frac{partial delta vec{v}}{partial t } + H vec{X} cdot nabla delta vec{v} + H delta vec{v} = - nabla delta phi, qquad tag{2}
$$

$$
nabla^2 delta phi = 4pi G delta rho. qquad tag{3}
$$

Weinberg applies the following Fourier transform to these equations,

$$ f(vec{X},t) = int exp left( frac{i vec{q} cdot vec{X}}{a} right) f_{vec{q}}(t) mathrm{d}^3vec{q} $$,

where $f(vec{X},t)$ is a place holder for $delta vec{v}, delta rho, $ and $delta phi$.

The resulting equations he gets are,

$$
frac{mathrm d delta rho_{vec{q}}}{mathrm d t } + 3 H delta rho_{vec{q}} + frac{ibar{rho}}{a} vec{q} cdot delta vec{v}_{vec{q}} = 0 qquad tag{1'}$$

$$
frac{mathrm d delta vec{v}_{vec{q}}}{mathrm d t } + H delta vec{v}_{vec{q}} = -frac{i}{a} vec{q} delta phi_{vec{q}} qquad tag{2'}$$

$$
vec{q}^2 delta phi_{vec{q}} = -4pi G a^2 delta rho_{vec{q}} qquad tag{3'}$$.

For the most part these new equations can be obtained by making the substitution $nabla rightarrow i vec{q}/a$.

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My question : There doesn't seem to be any terms in the transformed equations which correspond to the terms $ H vec{X} cdot nabla delta rho$ and $H vec{X} cdot nabla delta vec{v}$. Weinberg makes no comment about their absence. Is anyone aware of a legitimate mathematical reason for these terms to disappear in the transformed equations?