Double extrasolar planets

I am very interested in double planets. I am curious if there is currently a way that a Jupiter-sized system of double extrasolar planets (or something of that nature) could be found with today's current methods. I can understand that a transit can be a good way, but what about Doppler?

Another question, what if a transiting planet showed very strong evidence of being a double planet (maybe with the primary planet being the mass of Jupiter and the secondary being Neptune), what would it look like when the planet was looked upon by Doppler telescopes? Would it be shown that the planet is a double, would it look inconclusive, or would it look like one planet?

At the moment nothing has been detected. A tentative Trojan exoplanet has been inferred in Tau1 Gruis system but no confirmation has come so far.

Edasich wrote:

At the moment nothing has been detected. A tentative Trojan exoplanet has been inferred in Tau1 Gruis system but no confirmation has come so far.

How does "trojan planet" answer my question about "double planets"? I joke, but my question was: if a transiting planet showed strong evidence of being a double planet, that when the scientists looked at its Doppler measurements, what would it look like? This is only a hypothetical scenario. Would the Doppler readings show that it is a double planet? Would the reading be incunclusive? Or would the reading only support one planet (even tough there clearly is two)?

In a double planet, the radial velocity wouldn't appear too different, at least no more different than a planet with a giant moon. Differentiating between double planets is similar to attempting to detect extrasolar moons, which has not been done. I would tentatively say the only way to detect it is via high-resolution direct imaging, or transit light curve.

Stepping out of the bounds of what might be realistic, I'm guessing close double planets produce gravity waves that would propagate through the system. Perhaps this is sufficient to slightly modify the orbits of other planets in the system. Perhaps this might be detected with radial velocity.