Kapitan,
The RINS (Russian Institute for Naval Studies, and yes, I just made that up) have been analyzing your tactical problem. We believe that the Arleigh Burke can be defeated by employing our newest tactic; the Bracket Attack™.
Try hiding below the layer (If you have one) and fire 2-4 65cm torpedoes at him. Target one at him, a snapshot on both sides, and your final 65cm should enable well behind him. If he runs left, right, or away he'll eat a 65cm. If that fails you could simply load your internal and external tubes with SS-N-27 Anti-ship missiles, and set the enable to 10 nmi.
As soon as you fire make a hard course change. If he fires on you, launch one active and one passive countermeasure. Then order 300m and put the hammer down.