what recourse does a homeowner have you your Neighbor's cattle constantly get out and destroy your manicured Lawn ?

I've spent hundreds of dollars on Lawn seed, fertilize, and lime. I've aerated and spent hundreds on watering. The Neighbor has cattle and they have recently gotten out 4 times. They are destroying my lawn. He promised me after the second time, it would never happen again. He feels bad but all I get is I'm sorry.