Invariants of two- and three-dimensional hyperbolic equations
Date
2009ISSN
0022-247XSource
Journal of Mathematical Analysis and ApplicationsVolume
349Issue
2Pages
516-525Google Scholar check
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We consider linear hyperbolic equations of the formut t = underover(∑, i = 1, n) uxi xi + underover(∑, i = 1, n) Xi (x1, ..., xn, t) uxi + T (x1, ..., xn, t) ut + U (x1, ..., xn, t) u . We derive equivalence transformations which are used to obtain differential invariants for the cases n = 2 and n = 3. Motivated by these results, we present the general results for the n-dimensional case. It appears (at least for n = 2) that this class of hyperbolic equations admits differential invariants of order one, but not of order two. We employ the derived invariants to construct interesting mappings between equivalent equations. © 2008 Elsevier Inc. All rights reserved.