Letter to the Editor on Results Phys. 52, 106822 (2023) and beyond: In pursuit of a (3+1)-dimensional generalized nonlinear evolution system for the shallow water waves

Results Phys. 52, 106822 (2023) has initiated the readers into a good study of certain homoclinic breathers and rational solitons for a (3+1)-dimensional nonlinear soliton equation in the shallow water. Nevertheless, this Letter highlights the existence of a (3+1)-dimensional generalized nonlinear evolution system for the shallow water waves, which fully covers the aforementioned equation. For that generalized system, based on the computerized symbolic computation and singular manifold, this Letter accomplishes an auto-Backlund transformation coupled with some solitons beyond the travelling waves. Results are associated with the coefficients in that generalized system.

Automated summary

This letter discusses the existence of a (3+1)-dimensional generalized nonlinear evolution system for shallow water waves, and utilizes computerized symbolic computation and singular manifold to study the auto-Backlund transformation and the presence of solitons.