Changing search method

[german]

I would like you guys to help me finding out how to modify the search function of MegaShop theme as I need it to work in the following way:
 

The search should be able to find words parts. In example, If the user writes "hi he", the search should find "high heels". This should work also in other orders, lets say "he hi" would return also "high heels". and all the articles that match these syllables in different words. 
 

Inside /root/modules/tptnsearch the file "tptnsearch-ajax-php contains:

<?php

require_once('../../config/config.inc.php');
require_once('../../init.php');
require_once(dirname(__FILE__).'/tptnsearch.php');

$tptnsearch = new TptnSearch();
$result_products = array();
$products = array();
$tptnsearch_key = Tools::getValue('search_key');
$context = Context::getContext();
$count = 0;
$product_link = $context->link;

if (Tools::strlen($tptnsearch_key) >= 3) {
    $products = Product::searchByName($context->language->id, $tptnsearch_key);
    $total_products = count($products);
    if ($total_products) {
        for ($i = 0; $i < $total_products; $i++) {
            if (($products[$i]['name']) && ($products[$i]['active'])) {
                $images = Image::getImages($context->language->id, $products[$i]['id_product']);
                $product = new Product($products[$i]['id_product']);
                $products[$i]['link'] = $product_link->getProductLink($products[$i]['id_product'], $product->link_rewrite[1], $product->id_category_default, $product->ean13);
                $products[$i]['link_rewrite'] = $product->link_rewrite[1];
                $products[$i]['id_image'] = $images[0]['id_image'];
                $products[$i]['price'] = Tools::displayPrice(Tools::convertPrice($products[$i]['price_tax_incl'], $context->currency), $context->currency);
                if ($count < Configuration::get('TPTN_SEARCH_COUNT')) {
                    $result_products[] = $products[$i];
                    $count ++;
                } else {
                    break;
                }
            }
        }
    }

    $context->smarty->assign(array(
        'enable_image' => Configuration::get('TPTN_SEARCH_IMAGE'),
        'enable_price' => Configuration::get('TPTN_SEARCH_PRICE'),
        'enable_name' => Configuration::get('TPTN_SEARCH_NAME'),
        'search_alert' => $tptnsearch->no_product,
        'link' => $context->link,
        'products' => $result_products,
    ));

    $context->smarty->display(dirname(__FILE__).'/views/templates/hook/popupsearch.tpl');
} else {
    echo '<div class="wrap_item">'.$tptnsearch->three_character.'</div>';
}

I think changes must be done within this file. 

I would really appreciate any help you could give me.