Letter to the Editor on an extended time-dependent (3+1)-dimensional shallow water wave equation in an ocean or a river

Abstract

Of current fluid-dynamics interest, Results Phys. 41, 105937 (2022) has presented an extended time-dependent (3+1)-dimensional shallow water wave equation in an ocean or a river, with some solitons, breathers, lump waves and mixed breather-soliton solutions constructed under a certain condition. In this Letter, we call the attention that such a newly-proposed equation deserves more efforts, since that equation is thought to be possibly useful in a variety of the physical situations with an environmental impact, such as the flood, tsunamis as well as other flows in rivers and oceans. With the singular manifold and symbolic computation, we carry out an auto-Bäcklund transformation with some solitons for that equation. Both the Bäcklund transformation and solitons rely on the time-dependent coefficients.

Keywords

• Water waves in ocean or river
• Extended time-dependent (3+1)-dimensional shallow water wave equation
• Auto-Bäcklund transformation with solitons
• Singular manifold and symbolic computation