N-soliton evolution for a nonlinear dispersive long wave system

Applying the variable transformations and the improved Hirota method, two types of the N-soliton solutions, namely, smooth and singular N-soliton solutions are obtained for a nonlinear dispersive long wave system. The solutions can be expressed explicitly. Furthermore, the evolution processes are investigated for the N-soliton solutions. The result shows that the solitons will fission with time variable.