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Found 4 essays matching the above criteria.

  1. 1. 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

  3. 2. Solving Korteweg-de Vries equations with Discontinuous Galerkin methods

    University essay from Linköpings universitet/Tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Author : Markus Hellberg Mediaa; [2023]
    Keywords : Discontinuous Galerkin; Korteweg-de Vries; Conservation Laws; Partial Differential Equations; Numerical methods; Higher order spatial derivative; Heat Equation; Burgers’ Equation; Collocation; Lobatto Gauss Legendre; Stiffness; Nodal Approximation; Finite Volume; Finite Element;

    Abstract : In this thesis the Discontinuous Galerkin approximation performance applied to the Korteweg–de Vries equation is investigated. This equation is nonlinear with a third spatial derivative and can be used for shallow water movement. READ MORE

  4. 3. Introduction to the Hirota Direct Method

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Pascal Capetillo; Jonathan Hornewall; [2021]
    Keywords : ;

    Abstract : The primary subject matter of the report is the Hirota Direct Method, and the primary goal of the report is to describe and derive the method in detail, and then use it to produce analytic soliton solutions to the Boussinesq equation and the Korteweg-de Vries (KdV) equation. Our hope is that the report may also serve as an introduction to soliton theory at an undergraduate level. READ MORE

  5. 4. 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