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.

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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.