A low power density single-pulse laser irradiation of the Si surface has been used for the study of formation and self-organization of silicon nanotips. A two dimensional regular array of hillock-like nanotips has been created in the central region, a disturbed array comprising crossed lines of hillocks in the near-central region, and the "V"-shaped array in the peripheral region. Therefore, the long-range organization of hillocks changes from the center toward the periphery, following the Gaussian-like laser power profile. The evolution of hillocks due to the flow instability of molten silicon is equivalent to the instability of a liquid layer falling down a vertical plate. The novel result is that the hillock-like soliton structures can be identified with the lump solitons resulting from the nonlinear hydrodynamic instability evolution. (C) 2011 Elsevier B. V. All rights reserved.