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

Autor:	Liao, Xian, Plum, Michael
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: The number of eigenvalues for more general cases is characterized. Some interesting examples of potentials with piecewise-constant amplitude and phase velocity functions are included
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.05186 Zobrazit plný text záznamu View this record from Arxiv