Dynamically added contents are to be enhanced in jQuery Mobile.
This was mostly done using ‘.trigger( “create” )’

But .trigger( “create” ) has been deprecated since 1.4 and replaced with ‘enhanceWithin()’

Here is a demo of dynamically adding collapsible and enhancing it.

jqm1.4x.enhanceWithin.html

<!doctype html>
<html lang="en">
<head>
  <meta charset="utf-8">
  <meta name="viewport" content="width=device-width, initial-scale=1">
  <title>enhanceWithin demo</title>
<link rel="stylesheet" href="http://code.jquery.com/mobile/1.4.2/jquery.mobile-1.4.2.min.css">
<script src="http://code.jquery.com/jquery-1.10.2.min.js"></script>
<script src="http://code.jquery.com/mobile/1.4.2/jquery.mobile-1.4.2.min.js"></script> 

<script>
	$.mobile.document.on("click", "#insert-content", function () {
		var $pageContent = $("#page-content");

		var countries =
			"<div>" +
			  "<div data-role='collapsible' data-collapsed='false'>" +
				"<h2>Countries</h2>" +
				"<ul data-role='listview'>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Australia'>Australia</a></li>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Russia'>Russia</a></li>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Paraguay'>Paraguay</a></li>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Belgium'>Belgium</a></li>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Democratic_Republic_of_the_Congo'>Congo</a></li>" +
				"</ul>" +
			  "</div>" +
			"</div>";

		var cities =
			"<div>" +
			  "<div data-role='collapsible' data-collapsed='false'>" +
				"<h2>Cities</h2>" +
				"<ul data-role='listview'>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Sydney'>Sydney</a></li>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Yekaterinburg'>Yekaterinburg</a></li>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Asuncion'>Asunci&oacute;n</a></li>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Liege'>Li&egrave;ge</a></li>" +
				  "<li><a href='http://en.wikipedia.org/wiki/Kinshasa'>Kinshasa</a></li>" +
				"</ul>" +
			  "</div>" +
			"</div>"; 

		$pageContent.append(countries).append(cities);
		$pageContent.enhanceWithin();

	});

</script>
</head>
<body>
 
 
<div data-role="page">
	<div data-role="header">
		<h2>jQuery Mobile 1.4.2 Example</h2>
	</div>
	<div role="main" class="ui-content" id="page-content">
		<p>
			Content will be added at runtime when you click the button below.
		</p>
		<p>
			<a href="#" id="insert-content" data-role="button">Insert</a>
		</p> 
	</div>
</div> 
</body>
</html>