Tell me about the sid effect of double jaw surgery ? what is the common things that might happen even after one month from surgery ?

Few things: I'm assuming you need this for jaw alignment. There is a lot that goes into this including orthodontics to correct your bite. You can expect to have your jaw wired shut after and being placed on a liquid/soft diet. There is usually significant pain which will be managed by medication. I would suggest that you discuss your expectations thoroughly with your surgeon before surgery.

1 month: By a month post-surgically you should be relatively comfortable. If your oral hygiene is immaculate your teeth and gums will be healthy. You may still have some limited range of motion. You may need Physical Therapy to aid your jaw muscles to adapt to their new tasks. There may be some lip or tongue numbness. But all-in-all you should be doing well.