Abstract
An algorithm is given to linearize nonlinear first order systems of partial differential equations admitting an infinite-parameter Lie group of point transformations. The associated infinitesimal operator must be a linear combination of commuting operators which individually are not necessarily admitted by the basic system, whereas the coefficients of the combination are given by arbitrary solutions of a suitable linear system. The procedure is based on the introduction of the canonical variables corresponding to the commuting operators. Within such a framework we reformulate a theorem already proved by Kumei and Bluman [ SIAM J. Appl. Math. 42 (1982)]. The paper concludes with some illustrative examples of the proposed algorithm.
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