Spectral Analysis for Matrix Hamiltonian Operators
Analysis of PDEs
2015-05-18 v2 Numerical Analysis
Spectral Theory
Abstract
In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for the three dimensional cubic equation. Though we focus on a proof of the 3d cubic problem, this work presents a new algorithm for verifying certain spectral properties needed to study soliton stability. Source code for verification of our comptuations, and for further experimentation, are available at http://www.math.toronto.edu/simpson/files/spec_prop_code.tgz.
Cite
@article{arxiv.1003.2474,
title = {Spectral Analysis for Matrix Hamiltonian Operators},
author = {Jeremy L. Marzuola and Gideon Simpson},
journal= {arXiv preprint arXiv:1003.2474},
year = {2015}
}
Comments
57 pages, 22 figures, typos fixed