Essays about: "soliton wave"

Found 4 essays containing the words soliton wave.

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

    University essay from KTH/Skolan för teknikvetenskap (SCI)

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

    Abstract : 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. READ MORE

  3. 2. 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

  4. 3. Numerical solutions to the Boussinesq equation and the Korteweg-de Vries equation

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Filip Sjölander; [2021]
    Keywords : ;

    Abstract : The aim of the report is to numerically construct solutions to two analytically solvable non-linear differential equations: the Korteweg–De Vries equation and the Boussinesq equation. To accomplish this, a range of numerical methods where implemented, including Galerkin methods. READ MORE

  5. 4. Quantum Compactons in an extended Bose-Hubbard model

    University essay from Institutionen för fysik, kemi och biologi

    Author : Peter Jason; [2011]
    Keywords : Bose-Hubbard model; extended Bose-Hubbard model; compactons; quantum compactons;

    Abstract : The Bose-Hubbard model is used to study bosons in optical lattices. In this thesis we will use an extended Bose-Hubbard model to study a type of completely localized solutions, called compactons. The compactons are a special case of the much studied solitons. The soliton is a familiar concept in non-linear physics. READ MORE