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Integrable hierarchies in the Lax/zero-curvature formalism

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FindlayI_0719_macs.pdf (774.5Kb)
Date
2019-07
Author
Findlay, Iain
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Abstract
This 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.
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http://hdl.handle.net/10399/4254
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©Heriot-Watt University, Edinburgh, Scotland, UK EH14 4AS.

Maintained by the Library
Tel: +44 (0)131 451 3577
Library Email: libhelp@hw.ac.uk
ROS Email: open.access@hw.ac.uk

Scottish registered charity number: SC000278

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  • Accessibility
  • Policies
  • Privacy & Cookies
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AboutCopyright
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