By means of the variable separation approach, a general variable separation solution of the (2+1)-dimensional dispersive long-wave equation is derived. Because of the existence of the arbitrary functions in the general solution, the multivalued functions can be used to construct a type of localized excitation, folded solitary waves (FSWs) and foldons. Two classes of novel localized coherent structures, like both the FSWs-antiFSWs and foldonsantifoldons solutions, are found by selecting appropriate functions. These new structures exhibit some novel interaction features.