Meridional surfaces and (1,1)-knots
  We determine all (1,1)-knots which admit an essential meridional surface, namely, we give a construction which produces (1,1)-knots having essential meridional surfaces, and show that if a (1,1)-knot admits an essential meridional surface then it comes from the given construction. 
Mario Eudave-Munoz and Enrique Ramirez-Losada