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Multidimensional integrable systems and deformations

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posted on 2023-04-28, 14:03 authored by Ben Gormley

Integrable systems are dynamical systems which can in some sense be ‘solved explicitly’. The classification and deformations of 1 + 1 dimensional systems has been studied by B. Dubrovin, his collaborators and many others extensively. The study of 2 + 1 dimensional systems is ongoing and this thesis provides classification results in 2 + 1 dimensional systems based on the novel approach by the Loughborough group (E. Ferapontov, K. Khusnutdinova, V. Novikov). This involves firstly applying the method of hydrodynamic reductions to the dispersionless part of the systems and secondly reconstructing integrable dispersive systems by deforming the corresponding hydrodynamic reductions.

Funding

EPSRC

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

Loughborough University

Rights holder

© Benjamin Gormley

Publication date

2022

Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of the degree of Doctor of Philosophy of Loughborough University.

Language

  • en

Supervisor(s)

Vladimir Novikov ; Evgeny Ferapontov

Qualification name

  • PhD

Qualification level

  • Doctoral

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