Functional spaces : a direct approach

In this thesis I define the notion of a functional tensor space, and derive the specific form of the Lie derivative (w.r.t. generalized vector fields) on the constructed spaces, giving them a Lie module structure over the Lie algebra of generalized vector fields. I also construct the Euler complex in a recursive manner using the celebrated Cartan formula, and write down the first three operators explicitly. I call the third one, the Takens operator. Then, in the context of functional spaces, I prove and use the fact, that a Hamiltonian structure of an evolution equation is invariant under the flow of the equation, to derive all Hamiltonian structures (up to a certain order) of KdV equation and the Boussinesq equation. These are well known examples for nonlinear completely integrable evolution equations.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2001

Author dc:creator

• Barakat, Mohamed

Contributors dc:contributor

• Plesken, Wilhelm

• info:eu-repo/classification/ddc/510
• Mathematik
• Funktionalraum
• Lie-Ableitung
• Vektorfeld

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121226%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:59441