Spectral analysis for matrix Hamiltonian operators

Spectral analysis for matrix Hamiltonian operators
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矩阵哈密顿算子的谱分析

DOI：
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发表时间：
2010
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影响因子：
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通讯作者：
G. Simpson
G. Simpson
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文献类型：
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作者：
J. Marzuola;G. Simpson

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本文研究了通过线性化关于孤子解的非线性Schrödinger方程生成的矩阵哈密顿量的谱性质。通过数值辅助证明，我们证明了三维三次方程不存在嵌入特征值。虽然我们关注的是三维立方问题的证明，但这项工作提出了一种新的算法来验证研究孤子稳定性所需的某些谱性质。验证我们的计算和进一步实验的源代码可在http://hdl.handle.net/1807/25174上获得。
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.