  We compute explicitly the Khovanov polynomials (using the computer program
from katlas.org) for the two simplest families of the satellite knots, which
are the twisted Whitehead doubles and the two-strand cables. We find that a
quantum group decomposition for the HOMFLY polynomial of a satellite knot can
be extended to the Khovanov polynomial, whose quantum group properties are not
manifest. Namely, the Khovanov polynomial of a twisted Whitehead double or
two-strand cable (the two simplest satellite families) can be presented as a
naively deformed linear combination of the pattern and companion invariants.
For a given companion, the satellite polynomial "smoothly" depends on the
pattern but for the "jump" at one critical point defined by the s-invariant of
the companion knot. A similar phenomenon is known for the knot Floer homology
and tau-invariant for the same kind of satellites.
