We present intensive quasi-simultaneous X-ray and radio monitoring of the narrow line Seyfert 1 galaxy NGC 4051, over a 16 month period in 2000-2001. Observations were made with the Rossi Timing X-ray Explorer (RXTE) and the Very Large Array (VLA) at 8.4 and 4.8 GHz. In the X-ray band NGC 4051 behaves much like a Galactic black hole binary (GBH) system in a `soft-state. In such systems, there has so far been no firm evidence for an active, radio-emitting jet like those found in `hard state GBHs. VLBI observations of NGC 4051 show three co-linear compact components. This structure resembles the core and outer hot spots seen in powerful, jet-dominated, extragalactic radio sources and suggests the existence of a weak jet. Radio monitoring of the core of NGC 4051 is complicated by the presence of surrounding extended emission and by the changing array configurations of the VLA. Only in the A configuration is the core reasonably resolved. We have carefully removed the contaminations of the core by extended emission in the various arrays. The resulting lightcurve shows no sign of large amplitude variability (i.e. factor 50 %) over the 16 month period. Within the most sensitive configuration (A array) we see marginal evidence for radio core variability of ~25% (~0.12 mJy at 8.4GHz) on a 2-week timescale, correlated with X-ray variations. Even if the radio variations in NGC 4051 are real, the percentage variability is much less than in the X-ray band. Within the B configuration observations, where sensitivity is reduced, there is no sign of correlated X-ray/radio variability. The lack of radio variability in NGC 4051, which we commonly see in `hard state GBHs, may be explained by orientation effects. Another possibility is that the radio emission arises from the X-ray corona, although the linear structure of the compact radio components here is hard to explain.
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