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 10 of 10 for “"Nonlinear Schrödinger equations"”.
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Mapping of wave systems to nonlinear Schrödinger equations
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1980.
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Bifurcations in nonlinear Schrödinger equations with double well potentials
In this thesis, we consider nonlinear Schrödinger equations with double well potentials with attractive and repelling nonlinearities. We discuss bifurcations along bound states, especially ground states and the first excited states, and also deal with orbital stability of the ground states. In …
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Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations
… norms of global solutions of solutions to nonlinear Schrödinger type equations which we can't bound from above by energy conservation. The growth of such norms gives a quantitative estimate on the low-to high frequency cascade which can occur due to the nonlinear evolution. In our work, we …
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Spectral continuation study of the temporally periodic solitons of the damped-driven nonlinear Schrödinger equations
… soliton solutions of the driven, damped nonlinear Schrödinger equations, both in the case of parametric driving and direct driving. We hope that this study is of interest not only in the context of the nonlinear Schrödinger equations but also separately as a study of an efficient …
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On some nonlinear partial differential equations for classical and quantum many body systems
… deals with problems arising in the study of nonlinear partial differential equations arising from many-body problems. It is divided into two parts: The first part concerns the derivation of a nonlinear diffusion equation from a microscopic stochastic process. We give a new method to show that …
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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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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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Initial and boundary value problems in two and three dimensions
… for the Laplace and the modified Helmholtz equations in the interior of an equilateral triangle; (b) presents the solution of the heat equation in the interior of an equilateral triangle; (c) computes the eigenvalues and eigenfunctions of the Laplace operator in the interior of an …
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Excitations in superfluids of atoms and polaritons
… rise to an effective potential and introduces a nonlinearity to the PDE. In both cases, i.e. equilibrium and non equilibrium, the main model corresponding to the semiclassical wave is the Gross-Pitaevskii equation (GPE), which includes certain mathematical adaptions depending on the physical …
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On the Eigenvalues of the Manakov System
We clear up two issues regarding the eigenvalue problem for the Manakov system; these problems relate directly to the existence of the soliton [sic] effect in fiber optic cables. The first issue is a bound on the eigenvalues of the Manakov system: if the parameter ξ is an eigenvalue, then it must …