Fission and Fusion Interaction Phenomena of the (2+1)-Dimensional Dispersive Long Wave Equations

With the aid of symbolic computation, the (2+1)-dimensional dispersive long-wave equations are investigated via Bäcklund transformation and the Hirota bilinear method, two types of new multiple soliton solutions with 2n + 1 arbitrary functions for that system are derived. Based on the derived solutions, abundant coherent structures like dromions, compactons and peakons are derived, and moreover, the fission and fusion interactions among different types of localized structures are discussed graphically, which might be helpful for understanding the travel of the shallow water wave.