  [Abridged] We consider the dynamics of a system of hot super-Earths or
Neptunes such as HD 40307. We show that, as tidal interaction with the central
star leads to small eccentricities, the planets in this system could be
undergoing resonant coupling even though the period ratios depart significantly
from very precise commensurability. In a three planet system, this is indicated
by the fact that resonant angles librate or are associated with long term
changes to the orbital elements. We propose that the planets in HD 40307 were
in a strict Laplace resonance while they migrated through the disc. After
entering the disc inner cavity, tidal interaction would cause the period ratios
to increase from two but with the inner pair deviating less than the outer
pair, counter to what occurs in HD 40307. However, the relationship between
these pairs that occurs in HD 40307 might be produced if the resonance is
impulsively modified by an event like a close encounter shortly after the
planetary system decouples from the disc. We find this to be in principle
possible for a small relative perturbation on the order of a few 1.d-3 but then
we find that evolution to the present system in a reasonable time is possible
only if the masses are significantly larger than the minimum masses and tidal
dissipation is very effective. On the other hand we found that a system like HD
40307 with minimum masses and more realistic tidal dissipation could be
produced if the eccentricity of the outermost planet was impulsively increased
to about 0.15. The form of resonantly coupled tidal evolution we consider here
is quite general and could be of greater significance for systems with inner
planets on significantly shorter orbital periods characteristic of for example
CoRoT 7 b.
