Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 31 for “"nonlinear Schrödinger equation"”.
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On the discrete nonlinear Schrödinger equation with PT-Symmetry
… scattering method for the nonlocal semi-discrete nonlinear Schrödinger equation (known as Ablowitz-Ladik equation) with parity-time symmetry proposed in Ablowitz and Musslimani’s paper. This includes the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data and the …
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On Multi-component Nonlinear Schrödinger Equation with PT-Symmetry
… generalisations of nonlocal reductions of the nonlinear Schrödinger equation with parity- time (PT)-symmetry related to symmetric spaces. This includes: the spectral properties of the associated Lax operator, Jost solution, the scattering matrix, the minimal sets of scattering data and the …
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The Structure of Multipulse Solitons in the Generalised Nonlinear Schrödinger Equation
… we perform a detailed study of the generalised nonlinear Schrödinger equation (GNLSE) with quartic dispersion and show that it supports infinitely many multipulse solitons for a wide parameter range of the dispersion terms. These solitons exist through the balance between the quartic and …
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The direct scattering study of the parametrically driven nonlinear Schrödinger equation
Includes abstract. Includes bibliographical references.
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Radial, vortex, and spiral solutions to the nonlinear Schrödinger equation and other reaction--diffusion systems
This dissertation explores various solutions to nonlinear reaction-diffusion systems, focusing primarily on the nonlinear Schrödinger equation. Three types of solutions are investigated: radial solutions (with no angular dependence), vortex solutions (with angular dependence but no radial phase …
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Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation Utilizing GPU-Accelerated High-Order Compact Numerical Integrators
… dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex …
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Asymptotic stability and completeness in 2D nonlinear Schrodinger equation
… the asymptotic stability of ground states of the nonlinear Schrödinger equation in space dimension two. Under our hypotheses, the result actually shows asymptotic completeness in the regime of small initial data, i.e. any small initial data evolves into a superposition of a solitary wave (ground …
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Parametrically driven dark solitons
… solitons described by the parametrically driven nonlinear Schrödinger equation. We prove that both types of dark solitons (the Bloch and Néel walls) are stable throughout their existence regions, and that in the region of their coexistence, a family of Bloch-Néel bound states exists, which is …
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ERROR BOUNDS OF COMPACT FINITE DIFFERENCE METHODS FOR SOME DISPERSIVE PDEs AND APPLICATIONS
… oscillatory dispersive PDEs, including the nonlinear Klein-Gordon equation in the nonrelativistic regime and the Zakharov system in the subsonic regime. Proofs of error estimate based on energy methods and cut-off techniques are presented, and numerical results are reported for verification …
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On long time dynamic and singularity formation of NLS
… the long time behavior of focusing mass critical nonlinear Schrödinger equation (NLS). We will focus on the singularity formation and long time asymptotics. To be specific, there are two parts in the thesis. In the first part, we give a construction of log-log blow up solutions which blow up at m …
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A hybrid model for large scale simulation of unsteady nonlinear waves
… by combining the derived fifth order Enhanced Nonlinear Schrödinger Equation based on Fourier transform (ENLSE-5F), the fully nonlinear Enhanced Spectral Boundary Integral (ESBI) method and its simplified version. The numerical techniques and algorithm for coupling three models on time scale …
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Applications of light propagation in novel photonic devices
… In particular, self-similar solutions to the nonlinear Schrödinger equation have been investigated as a means of avoiding distortions associated with high power pulse propagation in optical fibres. The results show that it is the interplay between the nonlinear and dispersive effects that …
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Numerical modelling of dispersion managed soliton transmission
… The numerical technique used to solve the nonlinear Schrödinger equation is also introduced. The recent developments in the use of dispersion managed solitons are reviewed before the numerical results are presented. The work in this thesis covers two main areas; (i) the use of a saturable …
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Ultracold quantum gases in one-dimensional optical lattice potentials : nonlinear matter wave dynamics
… potentials our system is described by a discrete nonlinear Schrödinger equation, whose dynamics is determined by the tunneling between adjacent lattice sites and the nonlinear phase evolution. In the main part of this thesis I report on the first experimental observation of nonlinear self-trapping …
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Numerically optimized implementations, mitigation and simulations of polarisation mode dispersion in real-time transmission systems
… as well as a method derived from the Manakov-PMD equation are implemented and investigated separately through the distribution of a state of polarisation on the Poincaré sphere, and the evolution of the dispersion of a signal. Next these two methods are statistically examined and compared to …
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Compactons in strongly nonlinear lattices
… work, we study wave phenomena in strongly nonlinear lattices. Such lattices are characterized by the absence of classical linear waves. We demonstrate that compactons – strongly localized solitary waves with tails decaying faster than exponential – exist and that they play a major role in …
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Multi-Symplectic Integrators for Nonlinear Wave Equations
… for Hamiltonian ordinary differential equations have shown to be robust, efficient and accurate in long-term calculations. In this thesis, we show how symplectic integrators have a natural generalization to Hamiltonian PDEs by introducing the concept of multi-symplectic partial …
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Numerical and asymptotic modeling of evolving nonlinear ocean surface wave fields
… is the asymptotic and numerical modeling of nonlinear ocean surface wave fields. In particular, a development of an accurate numerical model for the evolution of nonlinear ocean waves, including extreme waves known as Rogue/Freak waves. Due to their elusive and destructive nature, the media …
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Integrable Nonlinear Relativistic Equations
This work focuses on three nonlinear relativistic equations: the symmetric Chiral field equation, Einstein's field equation for metrics with two commuting Killing vectors and Einstein's field equation for diagonal metrics that depend on three variables. The symmetric Chiral field equation is …
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