The Integrability of Lie-invariant Geometric Objects Generated by Ideals in the Grassmann Algebra
作者:
D.L. Blackmore,
Y.A. Prykarpatsky,
R.V. Samulyak,
期刊:
Journal of Nonlinear Mathematical Physics
(Taylor Available online 1998)
卷期:
Volume 5,
issue 1
页码: 54-67
ISSN:1402-9251
年代: 1998
DOI:10.2991/jnmp.1998.5.1.6
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E.Cartan. Especially, the E.Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame work of the Wahlquist Estabrook prolongation structures on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation.
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