Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras

Abstract

Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear variable-coefficient evolution equations, both in 1+1 dimensions and in 2+1 dimensions, which possess higher-degree polynomial-in-time dependent symmetries. The theory also provides a kind of new realisation of graded Lie algebras. Some illustrative examples are given.

11 pages, latex, to appear in J. Phys. A: Math. Gen

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