On perturbations of the spectrum of one-dimensional PT-symmetric periodic Schrodinger operator

2025/10/21 by Grinevich, P. G., Taimanov, I. A.
#35C20 #37K15 #37K20 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2510.18349

Abstract

For PT-symmetric periodic Schrodinger operator, which is a small perturbation of the zero potential, we calculate the spectrum and the divisor of zeroes of the Bloch function in the leading order of the perturbation theory. In particular, we show that the analogs of lacunae of the Bloch spectrum are ellipses, and their focal points coincide with the branch points of the spectral curve.

Citations

• Finite-zone PT-potentials
• The finite gap method and the periodic Cauchy problem of 2+1 dimensional anomalous waves for the focusing Davey-Stewartson 2 equation
• The finite gap method and the analytic description of the exact rogue wave recurrence in the periodic NLS Cauchy problem. 1
• On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KdV potentials

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