Invariants of Hyperbolic Equations: Solution of the Laplace Problem

被引：21

作者：

N. Kh. Ibragimov

机构：

[1] Blekinge Institute of Technology,

来源：

Journal of Applied Mechanics and Technical Physics | 2004年 / 45卷 / 2期

关键词：

Laplace invariants; integration of hyperbolic equations; equivalence transformations; semi‐invariants;

D O I：

10.1023/B:JAMT.0000017577.36177.a2

中图分类号：

学科分类号：

摘要：

This paper gives a solution of the Laplace problem, which consists of finding all invariants of the hyperbolic equations and constructing a basis of the invariants. Three new invariants of the first and second orders are found, and invariant‐differentiation operators are constructed. It is shown that the new invariants, together with the two invariants detected by Ovsyannikov, form a basis such that any invariant of any order is a function of the basis invariants and their invariant derivatives.

引用

页码：158 / 166

页数：8

共 4 条

[1]

Ibragimov N. H.(1997)Infinitesimal method in the theory of invariants of algebraic and differential equations Notices South African Math. Soc. 29 61-70

[2]

Laguerre E.(1879)Sur quelques invariants des équations différentielles lin éaires Comp. Rend. Acad. Sci. Paris 88 224-227

[3]

Ovsyannikov L. V.(1960)Group properties of the Chaplygin equation J. Appl. Mech. Tech. Phys. 3 126-145

[4]

Ibragimov N. H.(2002)Laplace type invariants for parabolic equations Nonlinear Dyn. 28 125-133

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