Semiclassical WKB problem for the non-self-adjoint Dirac operator with analytic potential

Autor:	Fujiié, Setsuro, Kamvissis, Spyridon
Rok vydání:	2019
Předmět:	Mathematical Physics
Druh dokumentu:	Working Paper
DOI:	10.1063/1.5099581
Popis:	In this paper we examine the semiclassical behaviour of the scattering data of a non-self-adjoint Dirac operator with analytic potential decaying at infinity. In particular, employing the exact WKB method, we provide the complete rigorous uniform semiclassical analysis of the reflection coefficient and the Bohr-Sommerfeld condition for the location of the eigenvalues. Our analysis has some interesting consequences concerning the focusing cubic NLS equation, in view of the well-known fact discovered by Zakharov and Shabat that the spectral analysis of the Dirac operator is the basis of the solution of the NLS equation via inverse scattering theory. Comment: 37 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1904.05697 Zobrazit plný text záznamu View this record from Arxiv