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Multivectors with trivial values a the inverse scattering transform

Wisse, F (2018) Multivectors with trivial values a the inverse scattering transform. Bachelor's Thesis, Physics.

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Abstract

This is a research concerning 2 related but separate subjects in mathematics and theoretical physics. The mathemati- cal aspects concern geometry, algebra and analysis. The physical aspects concern Hamiltonian and Lagrangian systems. The first subject is variational multivectors on a jet space. We prove that variational multivectors with trivial values are themselves trivial. We accomplish this by finding a homotopy operator for variational multivectors. We find this homotopy operator by identifying varia- tional multivectors with horizontal differential forms on a jet space. To get more insight into homotopy operators, we first consider ex- amples on manifolds, jet spaces and super jet spaces. The second subject is the Inverse Scattering Transform as a method to solve a class of non-linear partial differential equations. We will use this method to find solutions of the Korteweg-de Vries equation.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Physics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:35
Last Modified: 15 Feb 2018 08:35
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/16429

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