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Zbl 0957.37025
Ma, W.X.; Bullough, R.K.; Caudrey, P.J.; Fushchych, W.I.
(Fushchich, V.I.)
Time-dependent symmetries of variable-coefficient evolution equations and graded Lie algebras. (English)
[J] J. Phys. A, Math. Gen. 30, No.14, 5141-5149 (1997). ISSN 0305-4470

This paper is devoted to polynomial-in-time dependent symmetries (ptd symmetries) for evolution equations with polynomial-in-time dependent coefficients. The author's provide a purely algebraic structure for constructing such integrable equations with these forms of symmetries. This guarantees existence of integrable equations in $1+1$ dimensions which possess these forms of symmetries and allows them to construct actual examples. To this end the authors use graded Lie algebras, and especially centreless Virasoro algebras.
[Messoud Efendiev (Berlin)]

MSC 2000:: *37C80 Symmetries, equivariant dynamical systems
17B70 Graded Lie algebras
17B68 Virasoro and related algebras
37J15 Symmetries, etc.

Keywords: evolution equations; symmetries; integrable equations; graded Lie algebras; Virasoro algebras

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