Wordpress default archive widget doesn't have any option for showing author archive widget. This small code snippet will convert default archive widget into a author archive widget. For showing the link I hooked only for month link, same filter can be applied to other archive link for day or year archive link for any author. This works on author…

gistfile1.php

add_filter('getarchives_where', 'getarchives_where_author');
add_filter('month_link', 'month_link_author');

/**
 * Custom function to filter query for author archive widget, this works on author page only
 *
 * @param $where
 * @return string
 */
function getarchives_where_author($where){
    global $wpdb, $wp_locale;
    if(is_author()){
        $curauth = (get_query_var('author_name')) ? get_user_by('slug', get_query_var('author_name')) : get_userdata(get_query_var('author'));
        //var_dump($curauth);
        $where .= ' AND post_author = '.$curauth->ID.' ';
    }
    return $where;
}

/**
 * Custom function to filter author archive link for month
 *
 * @param $link
 * @return string
 */
function month_link_author($link){
    global $wpdb, $wp_locale;
    if(is_author()){
        $curauth = (get_query_var('author_name')) ? get_user_by('slug', get_query_var('author_name')) : get_userdata(get_query_var('author'));
        //author_name=asaduzzeman
        if(strpos($current_url, '?') !== false) {
            $link .= '&author_name='.$curauth->user_login;
        }
        else{
            $link .= '?author_name='.$curauth->user_login;
        }

    }
    return $link;
}

This throws errors b/c $current_url is not set. But even if you set it, it doesn't work.