Consider taking a homeopathic tablet called “No-Jet-Lag” (http://www.nojetlag.com).
This product reportedly lessens the adverse effects of "jet-lag."
The tablet has been registered with the FDA since 1992 (http://www.magellans.com/store/jetlag).
Current thinking remains mixed on the effectiveness of melatonin, so make a note to chat with your physician about when to begin the medication, dosages, strength, etc. Supposedly, if you take it at the wrong time, it can worsen your condition.