How to Add Aditional Search Button?

I have added function to functions.php so authors can search only their published content;

function search_author($query) {
  if ($query->is_search) {
        $query->set('author', get_current_user_id());
  }
  return $query;
}
add_filter('pre_get_posts','search_author');

I would like to add additional “Search my posts” button to searchform.php so only logged in users would have this button for searching posts they published. But I can get it to work. 🙁
When I click on any button when logged in it searches author only.

searchform.php
————————————————————

<?php if ( is_user_logged_in() ) { ?>
<form action="<?php echo home_url(); ?>/" method="get" id="searchform">
    <fieldset>
        <div id="searchbox">
            <input class="input" name="s" type="text" id="keywords" value="<?php _e('Search input','mytheme') ?>" onfocus="if (this.value == '<?php _e('Search input','mytheme') ?>') {this.value = '';}" onblur="if (this.value == '') {this.value = '<?php _e('Search input','mytheme') ?>';}">
                </div>
                <div id="searchbutton1">
                <p class="button search">
            <input type="submit" name="search" value="<?php _e('Search All Posts','mytheme') ?> ">
                </p>
                </div>
                <div id="searchbutton2">
                <p class="button search">
            <input type="submit" name="author" value="<?php _e('Search My Posts','mytheme') ?> ">
                </p>
                </div>
        </fieldset>
</form>
<?php } else { ?>
<form action="<?php echo home_url(); ?>/" method="get" id="searchform">
    <fieldset>
        <div id="searchbox2">
            <input class="input" name="s" type="text" id="keywords" value="<?php _e('Search input','mytheme') ?>" onfocus="if (this.value == '<?php _e('Search input','mytheme') ?>') {this.value = '';}" onblur="if (this.value == '') {this.value = '<?php _e('Search input','mytheme') ?>';}">
                </div>
                <p class="button search2">
            <input type="submit" name="search" value="<?php _e('Search','mytheme') ?> ">
                </p>
        </fieldset>
</form>
<?php } ?>

Thank you for any suggestions.