Essays about: "soliton"

Showing result 6 - 10 of 17 essays containing the word soliton.

  1. 6. On a novel soliton equation, its integrability properties, and its physical interpretation

    University essay from KTH/Fysik

    Author : Alexander Fagerlund; [2022]
    Keywords : Calogero-Moser systems; Conservation laws; Elliptic dynamics; Fluid dynamics; Hamiltonian mechanics; Hyperbolic dynamics; Integrability; Lax pairs; Pole ansatz; Riemann-Hilbert problems; Solitons; Bevarandelagar; Calogero-Mosersystem; Elliptisk dynamik; Fluiddynamik; Hamiltonmekanik; Hyperbolisk dynamik; Integrabilitet; Laxpar; Polansats; Riemann-Hilbertproblem; Solitoner;

    Abstract : In the present work, we introduce a never before studied soliton equation called the intermediate mixed Manakov (IMM) equation. Through a pole ansatz, we prove that the equation has N-soliton solutions with pole parameters governed by the hyperbolic Calogero-Moser system. READ MORE

  3. 7. 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

  4. 8. A Numerical and Analytical Investigation of The sine-Gordon Equation and Its Soliton Solutions

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Peder Hårderup; William Brorsson; [2021]
    Keywords : ;

    Abstract : This thesis investigates the nonlinear partial differential equation known as sine-Gordon and its special soliton solutions.Simpler analytical results are derived and more advanced methods and their results are discussed. READ MORE

  5. 9. 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

  6. 10. Numerical Simulation of Soliton Tunneling

    University essay from

    Author : Matilda Tiberg; Elias Estensen; Amanda Seger; [2020]
    Keywords : soliton; GPE; gross pitaevskii; Schrödinger; step potential; summation by parts; SBP-SAT; Simultaneous approximation term; SAT; Projection; SBP-Projection; finite differences; boundary treatment; interface treatment;

    Abstract : This project studied two different ways of imposing boundary conditions weakly with the finite difference summation-by-parts (SBP) operators. These operators were combined with the boundary handling methods of simultaneous-approximation-terms (SAT) and the Projection to impose homogeneous Neumann and Dirichlet boundary conditions. READ MORE