laravel 5.1如何使用连接表进行搜索

Question

我需要让作者搜索加入书籍。 书籍搜索工作正在进行，但是当作者搜索时，我得到了空白 使用laravel 5.1

表格书

id
book_title
book_edition
book_isbn

表作者

id
first_name
last_name
auth_address

table books_authors_relationship

book_id
author_id

预订模型

    public function author()
        {
            return $this->belongsToMany('App\Author','books_authors_relationship')->withTimestamps();
        }
public function scopeSearchByKeyword($query, $search)
    {
        if ($search!='') {
            $query->where(function ($query) use ($search) {
                $query->where("book_title", "LIKE","%$search%")
                    ->orWhere("date_publication", "LIKE", "%$search%")
                    ->orWhere("book_isbn", "LIKE", "%$search%");
            });
        }
        return $query;
    }
}

作者模型

 public function Book(){
      return $this->belongsToMany('App\Book','books_authors_relationship')->withTimestamps();
   }

   public function scopeSearchByKeyword($query, $search)
   {
      if ($search!='') {
         $query->where(function ($query) use ($search) {
            $query->where("first_name", "LIKE","%$search%")
                ->orWhere("last_name", "LIKE", "%$search%")
                ->orWhere("auth_address", "LIKE", "%$search%")
                ->orWhere("auth_DOB", "LIKE", "%$search%");
         });
      }
      return $query;
   }

SearchController

public function search_book($id)
{
    $search = \Request::get('search');
    $sections = Section::find($id);
    $authors_list = Book::with('author')->get();
    $all_books = Book::SearchByKeyword($search)->withTrashed()->paginate(5);
    return view('libraryViewsContainer.admin_book',compact('all_books','sections','authors_list'));
}