The Integrability of Lie-invariant Geometric Objects Generated by Ideals in the Grassmann Algebra

DOI

10.2991/jnmp.1998.5.1.6How to use a DOI?

Abstract

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 CartanEhresmann connection theory on fibered spaces. General structure of integrable oneforms 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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - D.L. Blackmore
AU  - Y.A. Prykarpatsky
AU  - R.V. Samulyak
PY  - 1998
DA  - 1998/02/01
TI  - The Integrability of Lie-invariant Geometric Objects Generated by Ideals in the Grassmann Algebra
JO  - Journal of Nonlinear Mathematical Physics
SP  - 54
EP  - 67
VL  - 5
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1998.5.1.6
DO  - 10.2991/jnmp.1998.5.1.6
ID  - Blackmore1998
ER  -