Backlund transformation and some different types of N-soliton solutions to the (3+1)-dimensional generalized nonlinear evolution equation for the shallow-water waves

The (3 + 1)-dimensional generalized nonlinear evolution equation is investigated based on the Hirota bilinear method. N-soliton solutions, bilinear Backlund transformation, high-order lump solutions, and the interaction phenomenon of high-order lump solutions for this equation are obtained with the help of symbolic computation. Besides, some different types of periodic soliton solutions are studied. Analysis and graphical simulation are presented to show the dynamical characteristics of some different types of N-soliton solutions are revealed. Many dynamic models can be simulated by nonlinear evolution equations, and these graphical analyses are helpful to understand these models. Compared with the published studied, some completely new results are presented in this paper.

Automated summary

The (3 + 1)-dimensional generalized nonlinear evolution equation was investigated using the Hirota bilinear method, resulting in various types of solutions and their interactions analyzed through symbolic computation. The study revealed the dynamical characteristics of different types of soliton solutions, providing insights for simulating dynamic models. The paper presented some completely new results compared to previous studies.