New dynamical behaviors for a new extension of the Shallow water model

Abstract

The aim of this work, is to construct some novel solutions for a new extension of the shallow water model in (3+1)-dimensions. Based on two methods namely; simplified Hirota’s method and a long-wave method a class of solutions are reported. Multiple soliton solutions in complex form, breather wave, and mixed breather–soliton solutions are constructed by using simplified Hirota’s method. To explore rational solutions and construct a class of physical interaction phenomena, a long-wave method is applied to N-soliton solutions. To our knowledge, the addressed solutions in this article are novel. Moreover, to better realize the physical meaning of obtained solutions, all solutions are plotted in three-dimension. The obtained solutions may be used in a wide variety of physical scenarios relevant to the environment, including modeling of floods and tsunamis as well as flow in rivers and open channels.

Keywords

• Shallow water model
• Long-wave method
• Breather solution
• M-lump waves
• Mixed solutions
• Complex solutions