New soliton structures with non-propagating behavior in three-dimensional system

By means of a special variable separation approach, a general solution with some arbitrary functions of the three-dimensional Nizhnik–Novikov–Veselov equation is derived. Based on this solution, abundant non-propagating solitons (sometimes solitary waves may be more accurate), such as dromion, ring, peakon, compacton, and foldon, etc. are found by selecting appropriate functions.