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nlin.SI2018
On symmetric primitive potentials
Patrik Nabelek, Dmitry Zakharov, Vladimir Zakharov
The concept of a primitive potential for the Schroedinger operator on the line was introduced in [2,3,4]. Such a potential is determined by a pair of positive functions on a finite…
math.SP2018
A Riemann--Hilbert Problem Approach to Periodic Infinite Gap Hill's Operators and the Korteweg--de Vries Equation
Kenneth T-R. McLaughlin, Patrik V. Nabelek
We formulate the inverse spectral theory of infinite gap Hill's operators with bounded periodic potential as a Riemann--Hilbert problem on a typically infinite collection of spectr…