Sökning: "Nonlinear Schrödinger equation"

Visar resultat 1 - 5 av 6 uppsatser innehållade orden Nonlinear Schrödinger equation.

  1. 1. On the variational characterization of quasi-periodic standing waves of the nonlinear Schrödinger equation

    Kandidat-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Författare :Gustav Jillbratt; [2018]
    Nyckelord :Mathematics and Statistics;

    Sammanfattning : We consider quasi-periodic standing wave solutions U(t, x) = exp(i(ωt−px))Ψ(x) to the one-dimensional defocusing cubic nonlinear Schrödinger equation, where we assume that Ψ : R → C is 2π−periodic. We study a constrained minimization problem associated with these solutions, and we show that solutions with minimal period of Ψ(x) strictly less than 2π cannot be minimizers, whereas locally the minimum is obtained among those solutions with minimal period 2π. LÄS MER

  2. 2. Two variational problems related to the nonlinear Schrödinger equation

    Kandidat-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Författare :Oscar Stolpe; [2017]
    Nyckelord :Nonlinear Schrödinger equation; Standing waves; Bose-Einstein condensate; Variational problem; Elliptic functions; Mathematics and Statistics;

    Sammanfattning : The nonlinear Schrödinger equation is a partial differential equation which appears as a model in several branches of physics, including Bose-Einstein condensation and hydrodynamics. In this thesis, we investigate a particular class of solutions, namely periodic standing waves. LÄS MER

  3. 3. Numerical continuation of standing waves for the Davey-Stewartson equation

    Master-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Författare :Teo Nilsson; [2016]
    Nyckelord :Numerical continuation standing waves Davey Stewartson nonlinear Schrödinger equation ground excited state; Mathematics and Statistics;

    Sammanfattning : This thesis considers solitary standing wave solutions to the Davey-Stewart-son equation, which is a model for surface waves on a body of water in three dimensions. In a special case, the Davey-Stewartson equation is reduced to the well-known non-linear Schrödinger equation with cubic power which is known to have a countable familiy of radial standing waves. LÄS MER

  4. 4. Model of a Wave Diode in a Nonlinear System

    Kandidat-uppsats, Linköpings universitet/Linköpings universitet/Teoretisk FysikTekniska högskolan

    Författare :Erik Johansson; [2014]
    Nyckelord :Discrete Nonlinear Schrödinger Wave Diode Cubic Saturable Asymmetric Propagation;

    Sammanfattning : In this diploma work, two versions of the discrete nonlinear Schrödinger (DNLS) equation are used to model a nonlinear layered photonic crystal system; the cubic DNLS (cDNLS) equation and the saturable DNLS (sDNLS) equation. They both have site-dependent coefficients to break mirror symmetry with respect to propagation direction, as well as to describe the linear and nonlinear properties of the system. LÄS MER

  5. 5. Characterization of attractors in a model for boundary-driven nonlinear optical waveguide arrays with disorder, gain and damping

    Kandidat-uppsats, Linköpings universitet/Linköpings universitet/Teoretisk FysikTekniska högskolan

    Författare :Felix Faber; [2013]
    Nyckelord :waveguide arrays; nonlinear; disorder; gain; damping; randomly distributed potentials; DNLS; Discrete nonlinear Schrödinger equation;

    Sammanfattning : The purpose of this thesis is to study the effects of gain and damping on a nonlinear waveguide array with a strong disorder that is driven in the first site, and try to find regimes which have stable stationary solutions. This has been done with a modified DNLS (Discrete nonlinear Schrödinger equation). LÄS MER