LINEARIZATION PROCEDURE OF NONLINEAR 1ST-ORDER SYSTEM OF PARTIAL-DIFFERENTIAL EQUATIONS BY MEANS OF CANONICAL VARIABLES RELATED TO LIE-GROUPS OF POINT-TRANSFORMATIONS

[摘要] 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. (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-01