How to avoid the jquery "colorbox" closing when we are submitting the data

Question

i'm calling the external php page by using the ajax method in Jquery colorbox in that while i'm submitting the data the colorbox is closed automatically n go to the normal page view without lightbox how to avoid that and reopen the colorbox after submitting....

Please tell some suggestions r solutions abt this problems friends... //home page //jquery of colorbox

 <script src="jquery/jquery.colorbox-min.js"></script>
    <script>
        $(function(){
            $(".ajax").colorbox({width:"63%", height:"80%"})
        });
</script>
<a class="ajax" href="assign_ajax.php">New Task</a>

This is the the page called by ajax in colorbox while submitting it goes to the normal page out of colorbox im using //////////////////////////////ajax page///////////////////////

if(isset($_POST['update'])){ 

$sql = UPDATE `notes` SET `note`=$_POST['update_text'] WHERE`id`={$_GET['note_id']};
mysql_query($sql) or die(mysql_error());
}


<form name="update_form" id="update_form" action="<?php echo htmlspecialchars($_SERVER["PHP_SELF"]);>?note_id=<?php echo $row['id']; ?>" method="post">
<textarea name="update_text" id="update_text" rows="5" cols='55'><?php echo $row['note']; ?></textarea>
<br>
<input type="submit" id="update" name="update" value="update">
<input type="button" value="cancel" class ="edit" id="edit-<?php echo $row['id']; ?>">
</form>

Answer 1

<script src="jquery/jquery.colorbox-min.js"></script>
<script>
    function showColorBox(event)
    {
       event.preventDefault();
       $.colorbox({href:"assign_ajax.php"});
    }
</script>
<a class="ajax" onclick="showColorBox(event)">New Task</a>
//Or
<script src="jquery/jquery.colorbox-min.js"></script>
<script>
    $(function(){
        $(".ajax").on("click",function(event){
             event.preventDefault();
             $.colorbox({href:$(this).attr("href")});
        });
    });
</script>
<a class="ajax" href="assign_ajax.php">New Task</a>

EDIT

<?php
if(isset($_POST['update'])){ 
    $sql = "UPDATE `notes` SET `note`=$_POST['update_text'] WHERE`id`={$_GET['note_id']}";
    mysql_query($sql) or die(mysql_error());
}
?>


<form name="update_form" id="update_form" action="<?php echo htmlspecialchars($_SERVER['PHP_SELF']);>?" note_id="<?php echo $row['id']; ?>" method="post" onsubmit="return FALSE;">
<textarea name="update_text" id="update_text" rows="5" cols='55'><?php echo $row['note']; ?></textarea>
<br>
<input type="button" id="update" name="update" value="update">
<input type="button" value="cancel" class ="edit" id="edit-<?php echo $row['id']; ?>">
</form>
<script>
    $(function(){
        $("#update").on("click",function(){
             $.ajax({url: $("#update_form").attr("action"), data:{note_id: $("#update_form").attr("note_id"),update_text:$("#update_text").val()}, type:"POST", dataType:"json"}).done(function(data){});
        });
    });
</script>