Sökning: "soliton"

Visar resultat 1 - 5 av 17 uppsatser innehållade ordet soliton.

  1. 1. Investigation of soliton equations with integral operators and their dynamics

    Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)

    Författare :Ruben Vikars Hall; Carl Svennerstedt; [2023]
    Nyckelord :Soliton; Calogero-Moser-Sutherland system; Lax pair; Hilbert transform; Szegö projection; Benjamin-Ono equation; Non-chiral Intermediate long-wave equation; Szegö equation;

    Sammanfattning : We present Lax pairs and functions called Lax functions corresponding to Calogero- Moser-Sutherland (CMS) systems. We present the Benjamin-Ono (BO) equation and a pole ansatz to the BO equation, constructed from a specific type of Lax function called a special Lax function corresponding to Rational and Trigonometric CMS systems. LÄS MER

  3. 2. Numerical simulation of the non-linear Schrödinger equation A comparative study based on the summation-by-parts method in space and time

    Master-uppsats, Uppsala universitet/Institutionen för informationsteknologi

    Författare :Ibrohim Hamoud; [2023]
    Nyckelord :;

    Sammanfattning : In this work, we present the numerical implementation of various time marching methods based on the summation-by-parts (SBP) method for the time integration of nonlinear dispersive systems. More specifically, we consider the nonlinear Schrödinger (NLS) equation that accepts soliton or soliton-like solution as a primary case study. LÄS MER

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

    Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)

    Författare :Fredrik Jonsson; [2023]
    Nyckelord :;

    Sammanfattning : 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. LÄS MER

  5. 4. Numerical Simulation of the Generalized Modified Benjamin-Bona-Mahony Equation Using SBP-SAT in Time

    Kandidat-uppsats, Uppsala universitet/Avdelningen för beräkningsvetenskap

    Författare :Vilma Kjelldahl; [2023]
    Nyckelord :Benjamin-Bona-Mahony equation; non-linear; initial boundary value problem; summation-by-parts; simultaneous-approximation-term; time integration; simulation;

    Sammanfattning : This paper describes simulations of the generalized modified Benjamin-Bona-Mahony (BBM) equation, using finite difference methods (FDM). Well-posed boundary conditions (BCs) as well as stable semi-discrete approximations are derived using summations-by-parts (SBP) operators combined with the projection method. LÄS MER

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

    Master-uppsats, KTH/Fysik

    Författare :Anton Ottosson; [2022]
    Nyckelord :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;

    Sammanfattning : 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. LÄS MER