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arXiv · 1003.2474

Spectral Analysis for Matrix Hamiltonian Operators

Jeremy L. Marzuola·Gideon Simpson
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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.

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Jeremy L. Marzuola, Gideon Simpson. 2010-03-12. Spectral Analysis for Matrix Hamiltonian Operators. https://doi.org/10.1088/0951-7715%2F24%2F2%2F003

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