A new Lie algebra along with its induced Lie algebra and associated with applications

✍ Scribed by Binlu Feng; Jiaqi Liu

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 218 KB
• Volume: 16
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2010.07.024

✦ Synopsis

A 3 Â 3 Lie algebra H is introduced whose induced Lie algebra by decomposition and linear combinations is obtained, which may reduce to the Lie algebra given by AP Fordy and J Gibbons. By employing the induced Lie algebra and the zero curvature equation, a kind of enlarged Boussinesq soliton hierarchy is produced. Again making use of a subalgebra of the induced Lie algebra leads to the well-known KdV hierarchy whose expanding integrable system is also worked out. As an applied example of the Lie algebra H, we obtain a new integrable coupling of the well-known AKNS hierarchy.