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arXiv · 0906.0351

Dispersive estimates using scattering theory for matrix Hamiltonian equations

Jeremy Marzuola
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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 $\reals^3$. 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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Jeremy Marzuola. 2009-06-01. Dispersive estimates using scattering theory for matrix Hamiltonian equations. https://arxiv.org/abs/0906.0351

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