Spectral analysis for matrix Hamiltonian operators

In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schrodinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for the three dimensional cubic equation. Although 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 computations, and for further experimentation, is available at http://hdl.handle.net/1807/25174.

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