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dc.contributor.advisorDoikou, Anastasia
dc.contributor.authorFindlay, Iain
dc.date.accessioned2021-03-04T13:19:59Z
dc.date.available2021-03-04T13:19:59Z
dc.date.issued2019-07
dc.identifier.urihttp://hdl.handle.net/10399/4254
dc.description.abstractThis thesis focusses on the development of (1+1)-dimensional integrable hierarchies in both the classical and quantum settings via the Lax/zero-curvature picture, where the underlying Poisson structure is found through the use of a classical or quantum R-matrix. After setting the scene by using the non-linear Schrodinger and isotropic Landau-Lifshitz models as examples of the standard approach to constructing hierarchies in this picture, the focus shifts to two more recent developments: equal-space Poisson structures (and the resulting spatially conserved quantities and Lax pairs); and quantum Lax pairs, where previously only the quantum Lax matrix (the spatial component) was considered. The non-linear Schrodinger and isotropic Landau-Lifshitz models (or analogous quantum spin chains) are then used as examples for these recent developments to compare against the familiar results.en
dc.language.isoenen
dc.publisherHeriot-Watt Universityen
dc.publisherMathematical and Computer Sciencesen
dc.titleIntegrable hierarchies in the Lax/zero-curvature formalismen
dc.typeThesisen


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