Abstract
Based on three-wave method, abundant nonautonomous solutions with different wave structures of a 3D variable-coefficient generalized shallow water wave equation are presented. In this situation the basic configurations (characteristic, amplitude, and speed) of the nonautonomous waves mutate with time due to the effect of nonlinearity and dispersion. Discussions indicate the interaction between lump wave and a pair of resonance stripe solitons solutions, the interaction between lump wave and periodic wave solutions, and the breather-type periodic soliton solutions. The dynamic properties of the obtained solutions are demonstrated and analyzed graphically for different choices of the arbitrary functions in these solutions.