The authors of the study suggest that before going to bed, put your phone on silent (not vibrate). And to prevent the backlight from keeping you up, the authors recommend that you flip the phone screen side down, unless you need a night light.
Over two years ago, we asked the musical question, "Are you a sleep texter?" and told you that certain things (like texting, apparently) that don't require a lot of brain function, can be done in your sleep. This is a different, but related issue to the inability to get a good night's sleep if you text before bed. In this case, the solution is to move your handset out of reach before bedtime.
source: APA, Today via betabeat, Textually.org