Dispersive estimates using scattering theory for matrix Hamiltonian equations

Details Dispersive estimates using scattering theory for matrix Hamiltonian equations Dispersive estimates using scattering theory for matrix Hamiltonian equations

2009-06-01

arxiv.org/abs/0906.0351v1

Mathematics

Analysis of PDEs

48 pages, 3 figures

Scientific paper

We develop the techniques of \cite{KS1} and \cite{ES1} in order to derive dispersive estimates for a matrix Hamiltonian equation defined by linearizing about a minimal mass soliton solution of a saturated, focussing nonlinear Schr\"odinger equation {c} i u_t + \Delta u + \beta (|u|^2) u = 0 u(0,x) = u_0 (x), in $\reals^3$. These results have been seen before, though we present a new approach using scattering theory techniques. In further works, we will numerically and analytically study the existence of a minimal mass soliton, as well as the spectral assumptions made in the analysis presented here.

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