$("ul li#airlines-list.dropdown.hlink").addClass("open");

$(document).on('click', '#register-btn', function()
    {
        $("ul li#airlines-list.dropdown.hlink").addClass("open");
    });

<a id="register-btn" class="register-btn btn btn-custom btn-rnd animated
fadeInDown wow">Register</a>
<li id="airlines-list" class="dropdown hlink">
<a id="airlines-btn" href="#" data-toggle="dropdown" aria-expanded="true"><i class="ion-plane"></i>
</a>
<ul id="airlines" class="airlines dropdown-menu arrow">
//somestuff
</ul>
</li>