Two options:
#1
Have a look here. Click "Options" top right and select another langauges. Open a datebox plugin widget and it will be in the language you specified.
I like the way it's done using Crowdin, although you will end up with all your text in .js files. If you check out one of the languages sample files this will be a lot of meat to load if your site becomes more complex.
#2
Do this server side. I'm (using Coldfusion) loading a langauge object on first page load and cache this until the user selects a new language. My langauge object is about 60k with 2000 entries. You could also send this to the page from server via json and store it in the page, then you could reference it from Jquery/Javascript.
I will probably end up trying to switch from server side to using the first approach and will try to see if I can split up my language .js files according to JQM page and then load them together with require, which would mean only a few ks per page. If you don't mind having a bunch of langauge files for each language and page, this would probably be the best "Mobile" approach.