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.
Gao, XY; Guo, YJ; Shan, WR
Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto- and non-auto-Backlund transformations
Applied Mathematics Letters