Localized excitations with and without propagating properties in (2+1)-dimensions obtained by a mapping approach

By means of an extended mapping approach, a new type of variable-separation excitation is derived with two arbitrary functions in a (2+1)-dimensional modified dispersive water-wave system. Based on the derived variable-separation excitation, abundant nonpropagating and propagating solitons such as dromions, rings, peakons and compactons are revealed by selecting appropriate functions in this paper.