Something like this :

    var date = new Date('2013-02-11');        
    /* Add nr of days*/
    date.setDate(date.getDate() + 1);

    alert(date.toString());

I hope it helps.

I use something like:

new Date(dateObject.getTime() + amountOfDays * 24 * 60 * 60 * 1000)

Works with day saving time:

new Date(new Date(2014, 2, 29, 20, 0, 0).getTime() + 1 * 24 * 60 * 60 * 1000)

Works with new year:

new Date(new Date(2014, 11, 31, 20, 0, 0).getTime() + 1 * 24 * 60 * 60 * 1000)

It can be parametrized:

function DateAdd(source, amount, step) {
  var factor = 1;
  if (step == "day") factor = 24 * 60 * 60 * 1000;
  else if (step == "hour") factor = 60 * 60 * 1000;
  ...
  new Date(source.getTime() + amount * factor);
}

This is for 5 days:

var myDate = new Date(new Date().getTime()+(5*24*60*60*1000));

You don't need JQuery, you can do it in JavaScript, Hope you get it.

You can do:

function formatDate(date) {
    var d = new Date(date),
        month = '' + (d.getMonth() + 1),
        day = '' + d.getDate(),
        year = d.getFullYear();

    if (month.length < 2) 
        month = '0' + month;
    if (day.length < 2) 
        day = '0' + day;

    return [year, month, day].join('-');
}
 
console.log(formatDate('Sun May 11,2014'));

Usage example:

console.log(formatDate('Sun May 11,2014'));

Output:

2014-05-11

Demo on JSFiddle: http://jsfiddle.net/abdulrauf6182012/2Frm3/