To enable swipe gestures for page navigation in jQuery Mobile, use the swipeleft and swiperight events. Below is the exact implementation:
Basic Swipe Navigation
$(document).on("pagecreate", function() {
    $(document).on("swipeleft", ".ui-page", function(event) {
        var nextpage = $(this).jqmData("next");
        if (nextpage) {
            $.mobile.changePage(nextpage, { transition: "slide" });
        }
    });
    
    $(document).on("swiperight", ".ui-page", function(event) {
        var prevpage = $(this).jqmData("prev");
        if (prevpage) {
            $.mobile.changePage(prevpage, { transition: "slide", reverse: true });
        }
    });
});