The inverse of the usual recursion operator for the Korteweg-de Vries equation is applied to the Galilean symmetry. A new family of non-local symmetries results. A symmetry algebra isomorphic to the semidirect sum of the loop algebra over sl(2,R) and a subalgebra of the Virasoro algebra is found.
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Graeme Guthrie (1993) studied this question.
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