$( document ).on( "pagecreate", "#demo-page", function() {
    $( document ).on( "swipeleft swiperight", "#demo-page", function( e ) {
        // We check if there is no open panel on the page because otherwise
        // a swipe to close the left panel would also open the right panel (and v.v.).
        // We do this by checking the data that the framework stores on the page element (panel: open).
        if ( $( ".ui-page-active" ).jqmData( "panel" ) !== "open" ) {
            if ( e.type === "swipeleft" ) {
                $( "#right-panel" ).panel( "open" );
            } else if ( e.type === "swiperight" ) {
                $( "#left-panel" ).panel( "open" );
            }
        }
    });
});

<div data-role="page" id="demo-page" data-url="demo-page">
    <div data-role="header" data-theme="b">
        <h1>Swipe left or right</h1>
        <a href="#left-panel" data-icon="carat-r" data-iconpos="notext" data-shadow="false" data-iconshadow="false" class="ui-nodisc-icon">Open left panel</a>
        <a href="#right-panel" data-icon="carat-l" data-iconpos="notext" data-shadow="false" data-iconshadow="false" class="ui-nodisc-icon">Open right panel</a>
    </div><!-- /header -->
    <div role="main" class="ui-content">
        <dl>
            <dt>Swipe <span>verb</span></dt>
            <dd><b>1.</b> to strike or move with a sweeping motion</dd>
        </dl>
        <a href="#demo-intro" data-rel="back" class="back-btn ui-btn ui-corner-all ui-shadow ui-mini ui-btn-inline ui-icon-back ui-btn-icon-right">Back to demo intro</a>
    </div><!-- /content -->
    <div data-role="panel" id="left-panel" data-theme="b">
        <p>Left reveal panel.</p>
        <a href="#" data-rel="close" class="ui-btn ui-corner-all ui-shadow ui-mini ui-btn-inline ui-icon-delete ui-btn-icon-left ui-btn-right">Close</a>
    </div><!-- /panel -->
    <div data-role="panel" id="right-panel" data-display="push" data-position="right" data-theme="b">
        <p>Right push panel.</p>
        <a href="#" data-rel="close" class="ui-btn ui-corner-all ui-shadow ui-mini ui-btn-inline ui-icon-delete ui-btn-icon-right">Close</a>
    </div><!-- /panel -->
</div>

/* Swipe works with mouse as well but often causes text selection. */
/* We'll deny text selecton on everything but INPUTs and TEXTAREAs. */
#demo-page :not(INPUT):not(TEXTAREA) {
    -webkit-user-select: none;
    -moz-user-select: none;
    -ms-user-select: none;
    -o-user-select: none;
    user-select: none;
}
/* Content styling. */
dl { font-family: "Times New Roman", Times, serif; padding: 1em; }
dt { font-size: 2em; font-weight: bold; }
dt span { font-size: .5em; color: #777; margin-left: .5em; }
dd { font-size: 1.25em; margin: 1em 0 0; padding-bottom: 1em; border-bottom: 1px solid #eee; }
.back-btn { float: right; margin: 0 2em 1em 0; }