Live search results as you type... am I going about this the right way? jQuery + PHP

I have a search input and a hidden div. When you start typing in the search input, the hidden div becomes visible and results are brought in. In this case, I'm searching for client names.

It all works fine, however I think my code could be better but I'm not sure exactly where to begin. Each keyup requests a PHP script which accesses a table in a database to find a like string. But in my PHP script, I'm echo'ing some JS/jQuery which I'm not sure is good practice. Below is my code. Am I going about this the right way or am I totally off base? Any suggestions for improvement?

Javascript

$("#search").keyup(function() {
 $("#search_results").show("fast");
 $.ajax
 ({
  type: "POST",
  url: "http://localhost:8888/index.php/welcome/search/" + $("#search").val(),
  success: function(html)
  {
   $("#search_results").html(html);
  }
 });
});

PHP

function search($search_string = false)
    {
 if ($search_string)
 {
  $this->db->like('name', $search_string);
  $query = $this->db->get('clients');

  if ($query->num_rows() == 0)
  {
   echo "No client exists.";
  }
  else
  {
   foreach ($query->result() as $row)
   {
    echo '<script>';
    echo '
    $("#client_results_'.$row->id.'").hide();
    $("#'.$row->id.'").toggle(function()
    {
     $.ajax
     ({
      type: "POST",
      url: "http://localhost:8888/index.php/welcome/search_client_ads/" + '.$row->id.',
      success: function(html)
      {
       $("#client_results_'.$row->id.'").html(html).show("fast");
      }
     });
    }, function()
    {
     $("#client_results_'.$row->id.'").hide("fast").html("");
    });';
    echo '</script>';
    echo '<p><span id="'.$row->id.'">'.$row->name.'</span></p>';
    echo '<div id="client_results_'.$row->id.'"></div>';
   }
  }
 }
 else
 {
  echo '';
 }
}

function search_client_ads($client_id)
    {
 $query = $this->db->get_where('online_ads', array('client' => $client_id));

 if ($query->num_rows() == 0)
 {
  echo "No ads exist.";
 }
 else
 {
  foreach ($query->result() as $row)
  {
   echo $row->id;
  }
 }
}

Instead of returning numerous scripts, try returning a json string and having jquery loop through it.