Bilinear Auto-Bäcklund Transformations and Similarity Reductions for a (3+1)-dimensional Generalized Yu-Toda-Sasa-Fukuyama System in Fluid Mechanics and Lattice Dynamics - Gao, Xin-Yi; Guo, Yong-Jiang; Shan, Wen-Rui (Qualitative theory of dynamical systems, 2022)
Recent investigations on the liquids and lattices are both active. In this paper, with symbolic computation, we consider a (3+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama system for the interfacial waves in a two-layer liquid or elastic waves in a lattice, with two sets of the bilinear auto-Bäcklund transformations hereby built up. Moreover, we construct one set of the similarity reductions, from that system to a known ordinary differential equation. As for the amplitude or elevation of the relevant wave, our results rely on the coefficients in that system.