Abstract
This dissertation addresses the local-well posedness, singularity formation, and orbital stability of standing waves to inhomogeneous nonlinear dispersive equations. Inhomogeneous equations are equations with space-dependent coe
cients, which account for the impurities of the propagating media or the presence of an outer potential. Despite playing a crucial role in various domains in physics, the mathematical investigation of inhomogeneous dispersive equations has only started recently, and it is still in its early stages. In this dissertation, we investigate various properties of Schrödinger and Klein-Gordon equations.
cients, which account for the impurities of the propagating media or the presence of an outer potential. Despite playing a crucial role in various domains in physics, the mathematical investigation of inhomogeneous dispersive equations has only started recently, and it is still in its early stages. In this dissertation, we investigate various properties of Schrödinger and Klein-Gordon equations.
| Original language | English |
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| Qualification | Doctor of Philosophy |
| Awarding Institution |
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| Supervisors/Advisors |
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| Award date | 29 Nov 2019 |
| DOIs | |
| Publication status | Published - 2019 |
Keywords
- Schrodinger equation
- Klein-Gordon equation
- nonlinear partial dierential equation
- orbital stability
- singularity formation
- Hamiltonian systems
- ground states
- standing waves equation