Spectral Analysis for Matrix Hamiltonian Operators

Details Spectral Analysis for Matrix Hamiltonian Operators Spectral Analysis for Matrix Hamiltonian Operators

2010-03-12

arxiv.org/abs/1003.2474v2

Mathematics

Analysis of PDEs

57 pages, 22 figures, typos fixed

Scientific paper

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.

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