Author： Marzuola Jeremy L Simpson Gideon
Publisher： IOP Publishing
ISSN： 0951-7715
Source： Nonlinearity, Vol.24, Iss.2, 2011-02, pp. : 389-429
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Abstract
In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schrödinger 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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