Localized Excitations in (3+1) Dimensions: Dromions, Ring-Shape and Bubble-Like Solitons

By means of infinite-dimensional Kac-Moody-Virasoro symmetry group transformation, rich localized (3+1)-dimensional excitations such as dromions, ring-shape and bubble-like excitations are obtained for a matrix system which is produced by extending the Lax pair of the celebrated self-dual Yang-Mills field. Abundant (3+1)-dimensional localized excitations can also be found in other types of nonlinear systems.