Resonant multiple soliton, non-singular complexiton and singular complexiton solutions to the (3+1)-dimensional shallow water wave equation

The aim of the current research is to plumb some novel exact solutions to the (3+1)-dimensional shallow water wave equation. Taking advantage of the linear superposition theory and the weight algorithm, we derive the resonant multiple soliton solutions. On the basis of the constructed resonant multiple soliton solutions, a group of the complexiton solutions of the different types, namely the non-singular complexiton solutions and singular complexiton solutions, are extracted via drawing into the conjugate parameter pairs. The shapes of the developed explicit solutions are displayed by selecting the appropriate parameters. As we all know, the found exact solutions in this research are all new and have not yet appeared in other literature, which can do us good in understanding the nonlinear characteristic of the equation under explored.