Bilinear Auto-Bäcklund Transformations and Similarity Reductions for a (3+1)-dimensional Generalized Yu-Toda-Sasa-Fukuyama System in Fluid Mechanics and Lattice Dynamics

• Published in: Qualitative theory of dynamical systems Vol. 21; no. 4
• Main Authors: Gao, Xin-Yi, Guo, Yong-Jiang, Shan, Wen-Rui
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2022; Springer Nature B.V
• Subjects: Difference and Functional Equations; Differential equations; Dynamical Systems and Ergodic Theory; Elastic waves; Fluid dynamics; Fluid mechanics; Lattices; Mathematics; Mathematics and Statistics; Similarity; (3+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama system; 37K35; 37N10; Similarity reductions; 35Q35; 76B15; Symbolic computation; Lattice; Two-layer liquid; Bilinear auto-Bäcklund transformations
• ISSN: 1575-5460; 1662-3592
• DOI: 10.1007/s12346-022-00622-w

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.