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Showing 1 to 4 of 4 for “"Dispersive estimates"”.
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Dispersive Estimates for the Schrodinger Equation
Finally in Chapter 3 we consider a problem involving the non-linear Schrodinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, iut+dtu xx+u2u=0. We can reduce this to a non-linear, non-local eigenvalue equation that describes the …
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Dispersive estimates for the Schrödinger equation
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-30T12:54:50Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Green_William.pdf: 999536 bytes, checksum: 87eb33f24c92fd62a4874b5db34bf8da (MD5)
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Asymptotic Stability of the Ground States of the Nonlinear Schrodinger Equation
… are asymptotically stable. The proof hinges on dispersive estimates that we obtain for the time dependent, Hamiltonian, linearized dynamics around a careful chosen one parameter family of bound states that ""shadows"" the nonlinear evolution of the system. Due to the generality of the methods we …
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Estimates for solutions to the Dysthe equation and numerical simulations of walking droplets in harmonic potentials
… called rogue waves. In this thesis, we prove dispersive estimates and Strichartz estimates for the Dysthe equation. We then prove a Kato-type smoothing effect in which we are able to bound uniformly in space the L² norm in time of a fractional derivative of the linear solution by the L² norm …