In my experience, when you cancel you will receive a credit for the residual value less the change fee. That credit can be used to purchase any 1 or more tickets up to year after the original ticket issue. If the new ticket is less than the credit you will receive a voucher for the remaining balance which can be used, again, up to 1 year after the original ticket date.

The above is the usual. I have seen tickets that, when canceled, can only be used on the original route (my father booked a flight to SFO via Chase and had to cancel the return; the return could only be used ex-SFO). So when they do call to cancel, make sure to get the full rules.

I would also echo those above who mentioned waiting for a schedule change. That could turn the non-refundable ticket into a refundable ticket very easily.