Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto- and non-auto-Backlund transformations

In the Solar System, water and water waves are commonly seen: For the Earth, water is at the core of sustainable development and at the heart of adaptation to climate change; For the Enceladus, Cassini spacecraft discovers a possible global ocean of liquid water beneath an icy crust; For the Titan, Cassini spacecraft suggests an icy shell floating atop a global ocean. Shallow water waves near the ocean beaches or in the lakes can be described by the Boussinesq-Burgers-type equations. In this Letter, on the higher-order Boussinesq-Burgers system, symbolic computation helps us to go from the two-dimensional Bell polynomials to construct two non-auto-Backlund transformations and to proceed from the Painleve-Backlund format to obtain four auto-Backlund transformations with some soliton solutions. All of our results are shown to be dependent on the constant coefficient in the system. (C) 2019 Elsevier Ltd. All rights reserved.