Dispersive estimates using scattering theory for matrix Hamiltonian equations
arXiv:0906.0351
Abstract
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 Schrödinger equation {c} i u_t + Δu + β(|u|^2) u = 0 u(0,x) = u_0 (x), in . 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.
48 pages, 3 figures