You just have to add:
altField: "#my_hidden_input"
to your datepicker javascript constructor. I will look like:
$('#datepicker_1').datepicker({
dateFormat: 'yy-mm-dd',
showAnim: 'show',
minDate: '+0',
maxDate: '+2Y',
numberOfMonths: [1, $nomonth],
onClose: closeDatePicker_datepicker_1,
altField: "#my_hidden_input"
});