Fusionable and fissionable waves of (2+1)-dimensional shallow water wave equation

We investigate a (2+1)-dimensional shallow water wave equation and describe its nonlinear dynamical behaviors in physics. Based on the N-soliton solutions, the higher-order fissionable and fusionable waves, fissionable or fusionable waves mixed with soliton molecular and breather waves can be obtained by various constraints of special parameters. At the same time, by the long wave limit method, the interaction waves between fissionable or fusionable waves with higher-order lumps are acquired. Combined with the dynamic figures of the waves, the properties of the solution are deeply studied to reveal the physical significance of the waves.