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arXiv · 2207.05186

Eigenvalue analysis of the Lax operator for the one-dimensional cubic nonlinear defocusing Schr\"odinger equation

Xian Liao·Michael Plum
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Abstract

We characterize the location and number of eigenvalues for the Lax operator associated to the one-dimensional cubic nonlinear defocusing Schr\"odinger equation. With the help of a newly discovered unitary matrix, the analysis reduces to the study of the spectral problem for a unitarily equivalent operator, which involves only the amplitude and the phase velocity of the potential. Examples of potentials with special amplitude and phase velocity are investigated.

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Xian Liao, Michael Plum. 2022-07-11. Eigenvalue analysis of the Lax operator for the one-dimensional cubic nonlinear defocusing Schr\"odinger equation. https://arxiv.org/abs/2207.05186

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