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

W. X. Ma·R. K. Bullough·P. J. Caudrey·W. I. Fushchych
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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.

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W. X. Ma, R. K. Bullough, P. J. Caudrey, W. I. Fushchych. 1997-05-27. Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras. https://doi.org/10.1088/0305-4470%2F30%2F14%2F023

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