On the spectrum of the Lax operator of the Benjamin-Ono equation on the torus

2020/06/21 by Gérard, Patrick, Kappeler, Thomas, Topalov, Peter
#37K15 #47B35 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2006.11864

Abstract

We investigate the spectrum of the Lax operator L_u of the Benjamin-Ono equation on the torus for complex valued potentials u in the Sobolev space H^-s(\mathbbT,ℂ), 0 ≤ s < 1/2, with small imaginary part and prove analytic properties of the moment map, defined in terms of spectral data of L_u.

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