What was found
(CAN) WHILE LEVELING OFF AT 39,000 FT AFTER TAKEOFF OUT OF KONA HAWAII, THE CREW REPORTED THAT THE LT ENGINE N1, N2 AND ITT BECAME ERRATIC. THE LT ENGINE POWER ROLLED BACK TO BELOW 30 PERCENT N1. AS THE CREW WERE GOING THROUGH THE CHECKLIST THE LT ENGINE RE-LIT AND N1, N2 AND ITT RETURNED TO NORMAL AND STABILIZED FOLLOWED BY FADEC FAIL MESSAGE. THE CREW DECLARED AN EMERGENCY AND RETURNED WHERE AN UNEVENTFUL OVERWEIGHT, LANDING WAS PERFORMED WITH BOTH ENGINES RUNNING. CONDITIONS WERE REPORTED TO BE SMOOTH AIR WITH NO RAIN OR LIGHTNING. THE CREW REPORTED NO UNUSUAL NOISES OTHER THAN THE ENGINES OUT OF SYNC DURING THE EVENT. POST FLIGHT REVIEW OF THE ENGINE DOWNLOAD CONFIRMED A LT FLAMEOUT WITH ENGINE SPEED DROPPING DOWN TO 23 PERCENT N1, 41 PERCENT, N2 PRIOR TO RECOVERING. SEVERAL FAULTS WERE ALSO RECORDED INCLUDING SOME ECU CROSS CHANNEL COMMUNICATION FAULTS. BOTH ECUS WERE REPLACED TOGETHER WITH THE W3, W4, AND W5 HARNESSES AND THE ACFT RETURNED TO SERVICE.