SOURCE

$('#container').jstree({
  "plugins" : ["search"]
});
$("#s").submit(function(e) {
  e.preventDefault();
  $("#container").jstree(true).search($("#q").val());
});

<form id="s">
  <input type="search" id="q" />
  <button type="submit">Search</button>
</form>
<div id="container">
  <ul>
    <li data-jstree='{"opened":true}'>Root node
      <ul>
        <li>Child node 1</li>
        <li>Child node 2</li>
      </ul>
    </li>
  </ul>
</div>