Essays about: "Integrable Systems"

Showing result 1 - 5 of 10 essays containing the words Integrable Systems.

  1. 1. Integrability of super spin chains in 6D N=(1,0) SCFTs

    University essay from Uppsala universitet/Teoretisk fysik

    Author : Zuxian He; [2023]
    Keywords : 6D SCFTs; integrability; spin chains; representation theory; symmetry; oscillators; Lie algebra;

    Abstract : Superconformal field theories (SCFTs) are an important class of quantum field theories. These SCFTs have been a significant component in exploring and comprehending the fundamental framework of quantum field theories. READ MORE

  3. 2. Exact Solutions of Soliton Equations and Dynamical Systems

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Fredrik Jonsson; [2023]
    Keywords : ;

    Abstract : This report investigates how one can construct soliton solutions to the following solitonequations: the Korteweg-de Vries equation, the Benjamin-Ono equation, and the spinBenjamin-Ono equation by making rational pole ansätze, which are ansätze that dependon eponymous pole parameters moving in the complex plane. In doing so we demonstratea connection between these soliton solutions and the class of integrable dynamical systemsknown as Calogero-Moser systems. READ MORE

  4. 3. An Introduction to Hitchin Systems

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Manuel Neumayer; [2023]
    Keywords : Mathematics and Statistics;

    Abstract : This thesis aims to introduce the tools that are needed to understand — and historically led to the inception of — Hitchin systems. We lay out a basic theory of Hamiltonian systems on symplectic manifolds, and prove the Liouville-Arnold theorem, which states that integrable Hamiltonian systems admit coordinates in which their solution is basically linear. READ MORE

  5. 4. Crosscap States in Integrable Spin Chains

    University essay from KTH/Fysik

    Author : Christopher Ekman; [2022]
    Keywords : Theoretical Physics; Mathematical Physics; Integrability; Integrable Systems; Spin chains; Heisenberg model; Integrable Boundary States; Crosscap states; Teoretisk fysik; Matematisk fysik; Integrabilitet; Integrabla system; Spinnkedjor; Heisenbergmodellen; Integrabla gränstillstånd; Crosscaptillstånd;

    Abstract : We consider integrable boundary states in the Heisenberg model. We begin by reviewing the algebraic Bethe Ansatz as well as integrable boundary states in spin chains. Then a new class of integrable states that was introduced last year by Caetano and Komatsu is described and expanded. We call these states the crosscap states. READ MORE

  6. 5. A unified view of a family of soliton equations related to spin Calogero-Moser systems

    University essay from KTH/Fysik

    Author : Anton Ottosson; [2022]
    Keywords : Soliton equations; Solitons; Integrable systems; Spin Calogero-Moser systems; Exact solutions; Benjamin-Ono-type equations; Solitonekvationer; Solitoner; Integrerbara system; sCM-system; Exakta lösningar; Ekvationer av Benjamin-Ono-typ;

    Abstract : We study the interconnections between the spin Benjamin-Ono (sBO) and half-wave maps (HWM) equations, a pair of nonlinear partial integro-differential equations that have recently been found to permit multi-soliton solutions, where the time evolution of the constituent solitons can be described in terms of the well-known, completely integrable, spin Calogero-Moser (sCM) system. By considering a symmetry transformation of the sCM dynamics we are led to introduce a scale parameter into the sBO equation, yielding what we call the rescaled sBO (rsBO) equation, which has both the sBO and HWM equations as special cases. READ MORE