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Showing 1 to 20 of 20 for “"Nonlinear Schrodinger Equation"”.
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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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Study of the applications of the nonlinear Schrodinger equation.
Thesis (B.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1978.
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Asymptotic Stability of the Ground States of the Nonlinear Schrodinger Equation
"We consider a class of nonlinear Schrodinger equations in N = 3, 4, 5 space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in L2( RN )) nonlinearities. We study the asymptotic stability of …
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Boundary Controllability and Stabilizability of Nonlinear Schrodinger Equation in a Finite Interval
The dissertation focuses on the nonlinear Schrodinger equation iu_t+u_{xx}+kappa|u|^2u =0, for the complex-valued function u=u(x,t) with domain t>=0, 0<=x<= L, where the parameter kappa is any non-zero real number. It is shown that the problem is locally and globally well-posed for appropriate …
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Coupled mode reductions and rotating wave approximations in nonlinear equations
… of coupled mode theory in the cubic-quintic nonlinear Schrodinger/Gross Pitaevskii (NLS/GP) equation with a linear double-well potential and study justifications of the rotating wave approximations in lattice systems. First, we study the long-time dynamics near a symmetry breaking bifurcation …
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On Initial-Boundary Value Problems for the Nonlinear Schroedinger Equation and the Ginzburg-Landau Equation
… in this thesis. Well-posedness of the forced nonlinear Schrodinger equation (NLS) is shown in Chapter 1. The global solution to an initial-boundary value problem for the NLS is proved in Chapter 2. Global existence of the full-line problem for the Ginzburg-Landau equation (GL) is shown in …
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A new method of modelling tuneable lasers with functional composition
A new nonlinear model is proposed for tuneable lasers. Using the generalized nonlinear Schrodinger equation as a starting point, expressions for the transformations undergone by the pulse are derived for each of the five components (gain, loss, dispersion, modulation, and nonlinearity) within the …
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Variational Calculation of Optimum Dispersion Compensation for Nonlinear Dispersive Fibers
… data rate and distance. The principle nonlinear effect, called self-phase modulation, can also limit the system performance by causing spectral broadening. Hence, to achieve the optimal system performance, high data rate and low bandwidth occupancy, those effects must be overcome or …
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The development of nonlinear surface and internal wave groups
The development of nonlinear surface and internal wave groups is investigated. Surface wave evolution was observed in an unusually long wave channel as a function of steepness and group length. Dissipation and frequency downshifting were important characteristics of the long-time evolution. The …
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Stability of Periodic Waves in Nonlocal Dispersive Equations
… the existence and stability of periodic waves in equations that possess nonlocal dispersion, i.e. equations in which the dispersion relation between the temporal frequency, omega, and wavenumber, k, of a plane wave is not polynomial in ik. In models that involve only classical derivative operators …
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Electromagnetic waves in nonlinear and linear magnetooptic metamaterials
… models are outlined. An emphasisis placed on the nonlinear properties of metamaterials and their soliton propagationproperties. A thorough investigation of both temporal and spatial solitons is at the heart ofthis thesis, and in both cases the nonlinear Schrodinger equation is an appropriate …
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The nonlinear Schroedinger limit of the complex Ginzburg-Landau equation.
… of a study of the complex Ginzburg-Landau equation (CGL) as a perturbation of the nonlinear Schrodinger equation (NLS) in one dimension under periodic boundary conditions. Using an averaging technique which is similar to a Melnikov method for pde's, necessary conditions are derived for the …
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Classical and quantum nonlinear optics in confined photonic structures
Nonlinear optical phenomena associated with high-order soliton breakup in photonic crystal fibres and squeezed state generation in three dimensional photonic crystal microcavities are investigated. In both cases, the properties of periodically patterned, high-index contrast dielectric structures …
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Numerical and Analytical Studies of Electromagnetic Waves: Hermite Methods, Supercontinuum Generation, and Multiple Poles in the SEM
… order algorithms to solve partial differential equations (PDE). In the first chapter, we discuss the fundamentals of Hermite methods in great detail. Hermite interpolation is discussed as well as the different time evolution schemes including Hermite-Taylor and Hermite-Runge-Kutta schemes. …
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Localisation of Bose-Einstein condensates in optical lattices
… by a continuous model using the Gross-Pitaevskii equation in a modulated potential or, in the case of deep potentials, a discrete model using the Discrete Nonlinear Schrodinger equation. Spatially localised modes, known as lattice solitons in the continuous model, or discrete breathers in the …
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Measurement of the nonlinear refractive index (n2) and stimulated Raman scattering in optical fibers as a function of germania content, using the photorefractive beam coupling technique
… the understanding and control of optical fiber nonlinearities. While these nonlinearites limit the power handling capacity of optical fibers and can cause noise, signal distortion and cross talk in optically amplified transmission systems, they have been equally harnessed for the development of …
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Analytical and computational methods for the study of rare event probabilities in dispersive and dissipative waves
… the probabilities associated with rare events in nonlinear, large-dimensional lightwave systems that are driven by noise, including models for fiber-based optical communication system and mode-locked lasers. Throughout the last decade, IS has emerged as a valuable tool for improving the efficiency …
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Strongly Nonlinear Phenomena and Singularities in Optical, Hydrodynamic and Biological Systems
Singularity formation is an inherent feature of equations in nonlinear physics, in many situations such as in self-focusing of light nonlinearity is essential part of the model and physical events cannot be captured by linearized equations. There are nonlinear systems, such as $1$D NLSE where …
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Hamiltonian bifurcations in Schrodinger trimers
… space of the three-mode discrete NLS in the nonlinear regime with periodic boundary conditions is investigated by reducing the degree of freedom from three down to two. The families of standing waves are enumerated and normal forms are used to describe several families of relative periodic …