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 Schrodinger and Klein-Gordon equations.
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