Q:

Redirect to URL with variable inside php

I am trying to make a signon page, where people just type in their usernames and get redirected to a url with their username as a variable.
This should all happen without getting something from another file.
Just like, the form's action would be the php to redirect with the variable from the submit button.
I am not very much into php programming but know basic HTML and some jquery, so it would be awesome if there was anyone who could give me the code to copy/paste into my index file.
Thanks 
UPDATE:
As it is, i have the login system up and running, but it is located in the users own director.
So the form on the main page should load the username and paste it as an other directory on the server.

A:

<?php

        if(isset($_POST['action']) && $_POST['action']!="")
        {
            if(isset($_POST['username']) && $_POST['username']!="")
            {
             header('Location: some_other_page.php?username='.$_POST['username']);
             exit;
            }
        }

    ?>

    <form action='index.php' method='post'>
        <input name='username' type='text' value='' placeholder='Insert username here'>
        <input type='submit' value='Go' name='Go'>
        <input type='hidden' name='action' value='do_redirect'>
    </form>

