Geodesic
On spectral properties of the $L$ operator in the Lax pair of the sine-Gordon equation
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 4, pp. 452-509 
Thomas Kappeler; Yannick Widmer. On spectral properties of the $L$ operator in the Lax pair of the sine-Gordon equation. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 4, pp. 452-509. http://geodesic.mathdoc.fr/item/JMAG_2018_14_4_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We analyze the periodic spectrum of the $L$ operator in the Lax pair of the sine-Gordon equation in terms of the regularity of the potential.

[1] P. Djakov, B. Mityagin, “Instability zones of periodic 1-dimensional Schrödinger and Dirac operators”, Russian Math. Surveys, 61:4 (2006), 663–766 | DOI | MR | Zbl

[2] V. E. Zaharov, L. A. Tahtadžjan, L. D. Faddeev, “A complete description of the solutions of the “sine-Gordon” equation”, Dokl. Akad. Nauk SSSR, 219 (1974), 1334–1337 (Russian) | MR

[3] B. Grébert, T. Kappeler, The Defocusing NLS Equation and Its Normal Form, Lectures in Mathematics, European Mathematical Society, Zürich, 2014 | MR

[4] T. Kappeler, B. Mityagin, “Estimates for periodic and Dirichlet eigenvalues of the Schrödinger operator”, SIAM J. Math. Anal., 33:1 (2001), 113–152 | DOI | MR | Zbl

[5] T. Kappeler, J. Pöschel, KdV KAM, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer Verlag, New York, 2003 | Zbl

[6] T. Kappeler, F. Serier, P. Topalov, “On the characterization of the smoothness of skew-adjoint potentials in periodic Dirac operators”, J. Funct. Anal., 256:7 (2009), 2069–2112 | DOI | MR | Zbl

[7] V. Marchenko, Sturm-Liouville Operators and Applications, Operator Theory: Advances and Applications, 22, Birkhäuser, Basel, 1986 | DOI | MR | Zbl

[8] H. McKean, “The sine-Gordon and sinh-Gordon equations on the circle”, Comm. Pure Appl. Math., 34:2 (1981), 197–257 | DOI | MR | Zbl

[9] J. Pöschel, “Hill's potentials in weighted Sobolev spaces and their spectral gaps”, Math. Ann., 349:2 (2011), 433–458 | DOI | MR