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engBarakat, MohamedPlesken, WilhelmFunctional spaces : a direct approachinfo:eu-repo/classification/ddc/510MathematikFunktionalraumLie-AbleitungVektorfeldIn 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.Aachen : Publikationsserver der RWTH Aachen University 71 S. (2001). = Aachen, Techn. Hochsch., Diss., 2001info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersionPublikationsserver der RWTH Aachen University2001info:eu-repo/semantics/openAccessDEhttps://publications.rwth-aachen.de/record/59441https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121226%22StudentsStudent Financial Aid ProvidersTeachersResearchersinfo:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-2803