Walker wp_nav_menu submenu

Hello every one
im new in wordpress and i searched a lot how to do a custom menu form wp_nav_menu but i havent found an exemple to do submenu,
so here is my code:
wp_nav_menu(array('container' => false,'menu_id' => 'nav','depth' => 0,'menu_class' => 'sf-menu','walker' => new ik_walker()));
walker function

class ik_walker extends Walker_Nav_Menu{
	function start_lvl(&$output, $depth) {

			 $output .= '<ul id="nav" class="sf-menu">';
	}

	function end_lvl(&$output, $depth) {
		$output .= '</ul>';
	}

	//add the description to the menu item output
	function start_el(&$output, $item, $depth, $args) {
		global $wp_query;
		$indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';

		$class_names = $value = '';

		$classes = empty( $item->classes ) ? array() : (array) $item->classes;

		$class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item ) );
		$class_names = ' class="' . esc_attr( $class_names ) . '"';
 		if($item->title == 'Accueil')
 		{
			$output .= $indent . "<li class='current-menu-item'>";
		}
		else
		{
			$output .= $indent . "<li>";
		}

		$attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
		$attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
		$attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
		$attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';

		$item_output = $args->before;
		$item_output .= '<a'. $attributes .'>';
		$item_output .= $args->link_before . apply_filters( 'the_title', '<b>' . $item->title . '</b>', $item->ID ) . $args->link_after;
		$item_output .= '</a>';
		$item_output .= $args->after;

		$output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
	}

	function end_el(&$output, $item, $depth, $args) {

	}
}

i want to do test if the item if his children then i will change de class of ul to be a sub menu.