View Item 
        •   Utrecht University Student Theses Repository Home
        • UU Theses Repository
        • Theses
        • View Item
        •   Utrecht University Student Theses Repository Home
        • UU Theses Repository
        • Theses
        • View Item
        JavaScript is disabled for your browser. Some features of this site may not work without it.

        Browse

        All of UU Student Theses RepositoryBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

        Theory and experiments on soliton interactions

        Thumbnail
        View/Open
        bachelorThesisSimonVeldkamp (2).pdf (2.410Mb)
        Publication date
        2017
        Author
        Veldkamp, S.
        Metadata
        Show full item record
        Summary
        The behaviour of surfacewaves on shallow water is described by nonlinear differential equations. Putting a constraint on these equation, such that they only describe waves moving in a certain direction, one obtains the KdV-equation. This nonlinear partial differential equation has the surprising property that it admits stable solutions. In these solutions dispersive and nonlinear effects balance out, creating what is known as a soliton. For certain initial conditions the KdV-equation can be solved analytically by using the inverse scattering transform. This method shows that, for a certain initial condition, there is a one-to-one correspondence between the solitons that emerge from this condition, and the eigenvalues of the time-independent Schrodinger equation, where the potential is given by this initial condition. Furthermore, it shows that when co-propagating solitons overtake each other they maintain their shape and velocity, but obtain a phase difference. A solution for the system where waves are not constraint to a single direction has not been found yet. However using both numerical and analytic methods it has been shown that for both reflection at a vertical wall and head on collision between solitons, a phaselag occurs. Here experiments on reflection and head-on collisions of solitons are compared to these analytic and numerical results to show that indeed a phaselag occurs at reflection.
        URI
        https://studenttheses.uu.nl/handle/20.500.12932/26980
        Collections
        • Theses
        Utrecht university logo