making my search engine not refresh the page

Question

Hello,

I have a basic search engine and I was wondering if it can be done so I don't have to refresh my page, it also has a pagination to it.

This is my form.php

    <?php 
global $search_term;
global $location_term;
?>

<form action="index2.php" name="form" style="float:right;width:650px;height:60px;margin-right:30px;" onSubmit="return searchLocations();" >
<table style="float:right;"><tr>
<td>
  <label for="testinput"><b>Search</b> </label><br />
  </td>

  <td>
  <label for="testinput"><b>Location</b></label><br />
  </td></tr>
  <tr>
  <td>
  <input name="search_term" id="search_term" type="text" style="height:23px; margin-right:20px;font-size: 16px" value="<?PHP echo $search_term; ?>" size="36" autocomplete="off"/></td>
  <td>
  <input name="addressInput" id="addressInput" type="text" style="height:23px;margin-right:10px;font-size: 16px" value="<?PHP echo $location_term; ?>" size="36" autocomplete="off"/></td><td>

  <select id="radiusSelect">

      <option value="25" selected>25</option>
      <option value="100">100</option>

      <option value="200">200</option>

    </select>
    </td><td>

 <input type="submit" name="search_button" style= "padding: 5px; font-family: Arial, Helvetica, sans-serif; font-size: 12px;" value="Search" onClick="searchLocations();" />

  </td></tr></table>
</form>

and then here is my search_query.php

<?PHP
global $search_term;
global $location_term;
global $results;
function getmicrotime()
{
    list($usec, $sec) = explode(" ", microtime());
    return ((float)$usec + (float)$sec);
}
$connection_string = "connectionstring.php";
require_once($connection_string);
mysql_select_db("chef") or die ( 'Unable to select database.' );
$RESULTS_LIMIT=5;
if(isset($_GET['search_term']) && isset($_GET['addressInput']) && isset($_GET['search_button']))
{
      $search_term = $_GET['search_term'];
      $location_term = $_GET['addressInput'];

    if(isset($_GET['first_pos']))
    {
        $first_pos = $_GET['first_pos'];
    }
    else
    {
        $first_pos = 0;
    }

    $start_search = getmicrotime();
    $sql_query = mysql_query("SELECT * FROM searchengine WHERE MATCH(product) AGAINST('$search_term') AND MATCH(location) AGAINST('$location_term')");

    if($results = mysql_num_rows($sql_query) != 0)
            {
                $sql =  "SELECT * FROM searchengine WHERE MATCH(product) AGAINST('$search_term') AND MATCH(location) AGAINST('$location_term') LIMIT $first_pos, $RESULTS_LIMIT";
                  $sql_result_query = mysql_query($sql);   
            }
    else
            {
                  $sql = "SELECT * FROM searchengine WHERE (product LIKE '%".mysql_real_escape_string($search_term)."%' AND location LIKE '%".mysql_real_escape_string($location_term)."%') ";
                  $sql_query = mysql_query($sql);
                  $results = mysql_num_rows($sql_query);
                  $sql_result_query = mysql_query("SELECT * FROM searchengine WHERE (product LIKE '%".$search_term."%' AND location LIKE '%".$location_term."%') LIMIT $first_pos, $RESULTS_LIMIT ");
            }
    $stop_search = getmicrotime();
    $time_search = ($stop_search - $start_search);
}
?>

This is my pagination.php

<?PHP
global $first_pos;
global $sites;

if($first_pos > 0)
{
  $back=$first_pos-$RESULTS_LIMIT;
  if($back < 0)
  {
    $back = 0;
  }
  echo "<a href='index2.php?search_term=".stripslashes($search_term)."&addressInput=$location_term&search_button=Search&first_pos=$back' ></a>";
}
if($results>$RESULTS_LIMIT)
{
  $sites=intval($results/$RESULTS_LIMIT);
  if($results%$RESULTS_LIMIT)
  {
    $sites++;
  }
}
for ($i=1;$i<=$sites;$i++)
{
  $fwd=($i-1)*$RESULTS_LIMIT;
  if($fwd == $first_pos)
  {
      echo "<a href='index2.php?search_term=".stripslashes($search_term)."&addressInput=$location_term&search_button=Search&first_pos=$fwd '><b>$i</b></a> | ";
  }
  else
  {
      echo "<a href='index2.php?search_term=".stripslashes($search_term)."&addressInput=$location_term&search_button=Search&first_pos=$fwd '>$i</a> | ";   
  }
}
if(isset($first_pos) && $first_pos < $results-$RESULTS_LIMIT)
{
  $fwd=$first_pos+$RESULTS_LIMIT;
  echo "<a href='index2.php?search_term=".stripslashes($search_term)."&addressInput=$location_term&search_button=Search&first_pos=$fwd ' > >></a>";
  $fwd=$results-$RESULTS_LIMIT;
}
?>
    </td>
  </tr>
</table>

I was wondering how to make this search engine not refresh?