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

• Published in: Mathematical methods in the applied sciences Vol. 44; no. 14; pp. 11307 - 11323
• Main Authors: Han, Peng‐Fei, Bao, Taogetusang
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.09.2021
• Subjects: (3 + 1)‐dimensional generalized nonlinear evolution equation; Bäcklund transformation; Dynamic models; high‐order lump solutions; Hirota bilinear method; interaction phenomenon of high‐order lump solutions; Nonlinear evolution equations; periodic soliton solutions; Solitary waves; Transformations (mathematics); Water waves
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.7490

The (3 + 1)‐dimensional generalized nonlinear evolution equation is investigated based on the Hirota bilinear method. N‐soliton solutions, bilinear Bäcklund 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.