Multiple-soliton solutions, soliton-type solutions and rational solutions for the (3+1)-dimensional generalized shallow water equation in oceans, estuaries and impoundments

The Hirota bilinear method and Painleve-Backlund transformation are used to discuss the soliton solutions of the (3 + 1)-dimensional generalized shallow water equation. With the help of symbolic computation, multiple-soliton solutions, multiple singular soliton solutions, hyperbolic function solutions and trigonometric function solutions are formally obtained. These soliton solutions possess abundant physical architectures. The graphs corresponding to these solutions show the particular localized excitations and the interactions between two solitary waves and three solitary waves.