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Two types of new Lie algebras and corresponding hierarchies of evolution equations. (English) Zbl 1011.17018
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:
17B67Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
37K30Relations of infinite-dimensional systems with algebraic structures
35Q55NLS-like (nonlinear Schrödinger) equations
35K05Heat equation
17B80Applications of Lie algebras to integrable systems
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies