Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto- and non-auto-Bäcklund transformations. (June 2020)

• Record Type: Journal Article
• Authors: Gao, Xin-Yi; Guo, Yong-Jiang; Shan, Wen-Rui
• Is Part Of: Applied mathematics letters. Volume 104(2020)
• Publication Date: 2020-06
• Subjects: Solar system -- Water waves -- Symbolic computation -- The higher-order Boussinesq-Burgers system -- Auto- and non-auto-Bäcklund transformations -- Solitons; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106170
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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-Bäcklund transformations and to proceed from the Painlevé-Bäcklund format to obtain four auto-Bäcklund transformations with some soliton solutions. All of our results are shown to be dependent on the constant coefficient in the system.