Multiple soliton solutions and fusion interaction phenomena for the (2+1)-dimensional modified dispersive water-wave system

By means of Bäcklund transformation and the Hirota bilinear method, the (2+1)-dimensional modified dispersive water-wave system is investigated. With the aid of symbolic computation, new multiple soliton solutions with arbitrary functions are derived. Based on the derived solutions, rich coherent structures like dromions, peakons and compactons can be derived, and moreover, the fusion interactions among different types of localized structures are graphically studied, which might be helpful to understand the propagation processes for nonlinear and dispersive long gravity waves on shallow waters.