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Time-dependent symmetries of variable-coefficient evolution equations and graded Lie algebras. (English) Zbl 0957.37025
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.

37C80Symmetries, equivariant dynamical systems
17B70Graded Lie (super)algebras
17B68Virasoro and related algebras
37J15Symmetries, invariants, invariant manifolds, momentum maps, reduction
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