Waveguide arrays, their underlying Dirac equations and solitons living in the Dirac gap

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dc.contributor.advisorBarashenkov, Igor Vladilenovich
dc.contributor.authorDe Jager, Johannes Louis Wilhelmus
dc.date.accessioned2026-07-02T08:07:29Z
dc.date.available2026-07-02T08:07:29Z
dc.date.issued2026
dc.date.updated2026-07-02T07:59:30Z
dc.description.abstractThis thesis is a mathematical study of optical waveguide arrays, their underlying spinor equations, and soliton solutions. We discuss the origin and fundamental properties of the linear and nonlinear Dirac equations, including their invariances and the absence of analytical stability criteria. Equipped with an understanding of the properties of spinor solitons, we consider two novel waveguide structures. The first of these is a one-dimensional nonlinear waveguide array consisting of a pair of coupled periodic binary chains with a periodic variation of the propagation constant. This system is shown to reduce to the one-dimensional massive Thirring model. We present the derivation of soliton solutions of this system and examine their properties numerically. In the two-dimensional setting, we start by establishing the existence of Dirac equations in hexagonal lattices. Results of this analysis are used to study a novel waveguide array consisting of two hexagonal lattices stacked on top of each other with a unit offset and which has alternating gain and loss. We derive the stationary multivortex solutions of the two-dimensional Dirac equation arising in the array's continuum limit. Stability of these vortices is examined numerically by means of the Chebyshev spectral methods.
dc.identifier.apacitationDe Jager, J. L. W. (2026). <i>Waveguide arrays, their underlying Dirac equations and solitons living in the Dirac gap</i>. (). Unversity of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/43450en_ZA
dc.identifier.chicagocitationDe Jager, Johannes Louis Wilhelmus. <i>"Waveguide arrays, their underlying Dirac equations and solitons living in the Dirac gap."</i> ., Unversity of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2026. http://hdl.handle.net/11427/43450en_ZA
dc.identifier.citationDe Jager, J.L.W. 2026. Waveguide arrays, their underlying Dirac equations and solitons living in the Dirac gap. . Unversity of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/43450en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - De Jager, Johannes Louis Wilhelmus AB - This thesis is a mathematical study of optical waveguide arrays, their underlying spinor equations, and soliton solutions. We discuss the origin and fundamental properties of the linear and nonlinear Dirac equations, including their invariances and the absence of analytical stability criteria. Equipped with an understanding of the properties of spinor solitons, we consider two novel waveguide structures. The first of these is a one-dimensional nonlinear waveguide array consisting of a pair of coupled periodic binary chains with a periodic variation of the propagation constant. This system is shown to reduce to the one-dimensional massive Thirring model. We present the derivation of soliton solutions of this system and examine their properties numerically. In the two-dimensional setting, we start by establishing the existence of Dirac equations in hexagonal lattices. Results of this analysis are used to study a novel waveguide array consisting of two hexagonal lattices stacked on top of each other with a unit offset and which has alternating gain and loss. We derive the stationary multivortex solutions of the two-dimensional Dirac equation arising in the array's continuum limit. Stability of these vortices is examined numerically by means of the Chebyshev spectral methods. DA - 2026 DB - OpenUCT DP - University of Cape Town KW - Mathematics LK - https://open.uct.ac.za PB - Unversity of Cape Town PY - 2026 T1 - Waveguide arrays, their underlying Dirac equations and solitons living in the Dirac gap TI - Waveguide arrays, their underlying Dirac equations and solitons living in the Dirac gap UR - http://hdl.handle.net/11427/43450 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/43450
dc.identifier.vancouvercitationDe Jager JLW. Waveguide arrays, their underlying Dirac equations and solitons living in the Dirac gap. []. Unversity of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2026 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/43450en_ZA
dc.language.isoen
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.publisher.institutionUnversity of Cape Town
dc.subjectMathematics
dc.titleWaveguide arrays, their underlying Dirac equations and solitons living in the Dirac gap
dc.typeThesis / Dissertation
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMSc
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