Invariants of two- and three-dimensional hyperbolic equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:349

Article

Tsaousi, C.¹  Sophocleous, C.¹  Tracina, R.² 

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

[2] Dipartimento Matemat & Informat, I-95125 Catania, Italy

关键词: Hyperbolic equations;    Equivalence transformations;    Differential invariants;    Point transformations;   

DOI  :  10.1016/j.jmaa.2008.09.004

来源: Elsevier

【 摘 要 】

We consider linear hyperbolic equations of the form u(tt) = Sigma(n)(i=1) u(xixi) + Sigma(n)(i=1) X-i(x(1).....x(n).t) u(xi) + T (x(1).....x(n).t)u(t) + U(x(1)......x(n).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. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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