These docs are for an old release. Info on upgrading to v4
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next

Moves the calendar one step forward (by a month or week for example).

.fullCalendar( ‘next’ )

If the calendar is in month view, will move the calendar forward one month.

If the calendar is in basicWeek or agendaWeek, will move the calendar forward one week.

If the calendar is in basicDay or agendaDay, will move the calendar forward one day.

Example using next with an external button:

$('#my-next-button').click(function() {
  $('#calendar').fullCalendar('next');
});

View a demo that uses the prev and next methods.