Viewing the Solar System via a variable-coefficient nonlinear dispersive-wave system

Oceans crossing the Solar System attract people’s attention: the Earth, Enceladus, and Titan. On a variable-coefficient nonlinear dispersive-wave system for the shallow oceanic environment, our symbolic computation yields two non-auto-Bäcklund transformations and auto-Bäcklund transformations with some solitons, with regard to the wave elevation and surface velocity of the water wave, which depend on the variable coefficients. This paper could be of some use for the future oceanic studies in the Solar System.