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Zbl 1011.17018
Zhang, Yufeng
Two types of new Lie algebras and corresponding hierarchies of evolution equations. (English)
[J] Phys. Lett., A 310, No.1, 19-24 (2003). ISSN 0375-9601

Summary: An extension of the Lie algebra $A_{n-1}$ is proposed. As special cases, two new loop algebras are constructed, respectively. It follows that two types of new integrable Hamiltonian hierarchies are engendered. As their reduction cases, generalized nonlinear Schrödinger equations, coupled Fisher equations, and the standard heat-conduction equation are obtained, respectively. The method proposed can be used generally.

MSC 2000:: *17B67 Kac-Moody algebras
37K30 Relations with algebraic structures
35Q55 NLS-like (nonlinear Schroedinger) equations
35K05 Heat equation
17B80 Applications of Lie algebras to integrable systems
37K10 Completely integrable systems etc.

Keywords: integrable Hamiltonian hierarchies; loop algebras; reduction

Cited in: Zbl 1197.37083 Zbl 1135.37332

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