Engine Belts And Pulleys problems of the 1998 Hyundai Elantra

When driving at variable speeds, the engine cuts out then cuts back on. No consistencies to when or why it cuts out. Check engine light stays on for weeks at a time. Contacted dealer and have taken it in three times for this. Dealer apparently finds nothing wrong. First service, dealer kept car for 10 days only to replace the gas cap. Second and third visits found nothing to substantiate check engine light cause. Yet the check engine light comes on periodically and stays on for days. After 44000 miles, engine sounding different than when purchased. Burning smell comes form engine periodically, smells like a belt burning but no apparent belt is cinged. At times engine does not appear to change gears smoothly.