Abundant exact analytical solutions and novel interaction phenomena of the generalized (3+1)-dimensional shallow water equation

Abstract

This paper reveals abundant exact analytical solutions to the generalized (3+1)-dimensional shallow water equation. The generalized bilinear method is used in the solution process and the obtained solutions include the high-order lump-type solutions, the three-wave solutions, the breather solutions. The interaction between the high-order lump-type solutions and the soliton solutions is also elucidated. These solutions have greatly enriched the generalized (3+1)-dimensional shallow water equation in open literature.

Superposition Formulas and Evolution Behaviors of Multi-Solutions to the (3+1)-Dimensional Generalized Shallow Water Wave-like Equation

“…It is worth mentioning that the received multi-localized wave solutions and the interaction solutions are also the exact solutions of the GSWWE (2). In addition, the received results have enriched the exact solutions of the GSWWLE [69,70] and the GSWWE in the available literature.…”

“…When z = x, the rational solutions and the lump solutions of the GSWWLE (5) are studied [69]. The breather solutions, the three-wave solutions, the high-order lump-type solutions and the interaction solutions of the GSWWLE (5) are obtained in [70]. In the following, we will study new mixed solutions, the multi-localized wave solutions and the interaction solutions of the GSWWLE (5).…”