Folded solitary waves and foldons in the (2 + 1)-dimensional breaking soliton equation

Starting from the standard truncated Painlevé expansion, a Bäcklund transformation for the (2 + 1)-dimensional breaking soliton equation is derived. Making use of the variable separation approach, a variable separation solution of this model is obtained. By selecting appropriate multi-valued functions, a new class of localized coherent structures for the model are found. These structures exhibit interesting novel features not found in one-dimensions.