References
- Dubrovin BA. Periodic problems for the Korteweg–de Vries equation in the class of finite band potentials. Funct Anal Appl. 1975;9(3):215–223.
- Korotyaev E. Inverse problem and the trace formula for the Hill operator. II. Math Z. 1999;231(2):345–368.
- Trubowitz E. The inverse problem for periodic potentials. Commun Pure Appl Math. 1977;30(3):321–337.
- Zheludev VA. The spectrum of Schrödinger's operator, with a periodic potential, defined on the half-axis. (Russian) Works of Dept of Math Analysis of Kaliningrad State University. 1969:18–37.
- Korotyaev E, Schmidt KM. On the resonances and eigenvalues for a 1D half-crystal with localised impurity. J Reine Angew Math. 2012;670:217–248.
- Levitan BM. Inverse Sturm-Liouville problems. Translated from the Russian by O. Efimov. VSP, Zeist, 1987.
- Korotyaev E. Lattice dislocations in a 1-dimensional model. Commun Math Phys. 2000;213(2):471–489.
- Korotyaev E. Schrödinger operator with a junction of two 1-dimensional periodic potentials. Asymptot Anal. 2005;45(1–2):73–97.
- Dohnal T, Plum M, Reichel W. Localized modes of the linear periodic Schrödinger operator with a nonlocal perturbation. SIAM J Math Anal. 2009;41(5):1967–1993.
- Drouot A. The bulk-edge correspondence for continuous dislocated systems, Preprint, arXiv:1810.10603.
- Drouot A, Fefferman CF, Weinstein MI. Defect modes for dislocated periodic media, Preprint, arXiv:1810.05875.
- Hempel R, Kohlmann M. Spectral properties of grain boundaries at small angles of rotation. J Spectr Theory. 2011;1(2):197–219.
- Hempel R, Kohlmann M. A variational approach to dislocation problems for periodic Schrödinger operators. J Math Anal Appl. 2011;381(1):166–178.
- Hempel R, Kohlmann M, Stautz M, et al. Bound states for nano-tubes with a dislocation. J Math Anal Appl. 2015;431(1):202–227.
- Ablowitz MJ, Clarkson PA. Solitons, nonlinear evolution equations and inverse scattering. Cambridge: Cambridge University Press; 1991. (London mathematical society lecture note series; 149).
- Its AR, Kotljarov VP. Explicit formulas for solutions of the Schrödinger nonlinear equation. (Russian) Dokl Akad Nauk Ukrain SSR. 1976;Ser. A(11):965–968.
- Kotlyarov V, Its A. Periodic problem for the nonlinear Schrödinger equation, Preprint, arXiv:1401.4445.
- Previato E. Hyperelliptic quasiperiodic and soliton solutions of the nonlinear Schrödinger equation. Duke Math J. 1985;52(2):329–377.
- Bättig D, Grébert B, Guillot J-C, et al. Foliation of phase space for the cubic nonlinear Schrödinger equation. Comp Math. 1993;85(2):163–199.
- Grébert B, Guillot J-C. Gaps of one-dimensional periodic AKNS systems. Forum Math. 1993;5(5):459–504.
- Korotyaev E. Inverse problem and estimates for periodic Zakharov-Shabat systems. J Reine Angew Math. 2005;585:87–115.
- Korotyaev E. Marchenko-Ostrovski mapping for periodic Zakharov-Shabat systems. J Differ Equ. 2001;175(2):244–274.
- Misura T. Properties of the spectra of periodic and anti-periodic boundary value problems generated by Dirac operators. I, II. (Russian) Theor Funktsii Funktsional Anal i Prilozhen. 1978;30:90–101; 1979;31:102–109.
- Levitan BM, Sargsjan IS. Sturm-Liouville and Dirac operators. Dordrecht: Kluwer Academic Publishers Group; 1991. (Translated from the Russian. Mathematics and its applications (Soviet Series); 59).
- Teschl G. Renormalized oscillation theory for Dirac operators. Proc Amer Math Soc. 1998;126(6):1685–1695.
- Thaller B. The Dirac equation. Berlin: Springer-Verlag; 1992. (Texts and monographs in physics).
- Bingham NH, Goldie CM, Teugels JL. Regular variation. Cambridge: Cambridge University Press; 1989. (Encyclopedia of mathematics and its applications; 27).
- Korevaar J. Tauberian theory. A century of developments. Berlin: Springer-Verlag; 2004. (Grundlehren der Mathematischen Wissenschaften; 329).
- Seneta E. Regularly varying functions. Berlin: Springer-Verlag; 1976. (Lecture notes in mathematics; 508.
- Granata A. The problem of differentiating an asymptotic expansion in real powers. Part I: unsatisfactory or partial results by classical approaches. Anal Math. 2010;36(2):85–112.
- Kargaev P, Korotyaev E. Effective masses and conformal mappings. Commun Math Phys. 1995;169(3):597–625.
- Korotyaev E. Metric properties of conformal mappings on the complex plane with parallel slits. Internat Math Res Notices. 1996;1996(10):493–503.
- Weidmann J. Spectral theory of ordinary differential operators.Berlin: Springer-Verlag; 1987. (Lecture notes in mathematics; 1258.
- Reed M, Simon B. Methods of modern mathematical physics. IV. Analysis of operators. New York (NY): Academic Press [Harcourt Brace Jovanovich, Publishers]; 1978.
- Jittorntrum K. An implicit function theorem. J Optim Theory Appl. 1978;25(4):575–577.
- Kumagai S. Technical comment to: “An implicit function theorem”. J Optim Theory Appl. 1978;25(4):575–577.
- Krantz SG, Parks HR. The implicit function theorem. History, theory, and applications. Boston (MA): Birkhäuser Boston, Inc.; 2002.
- Hale JK. Ordinary differential equations. 2nd ed. Huntington (NY): Robert E. Krieger Publishing Co., Inc.; 1980.
- Pöschel J, Trubowitz E. Inverse spectral theory. Boston (MA): Academic Press, Inc.; 1987. (Pure and applied mathematics; 130.
- Grébert B, Kappeler T. The defocusing NLS equation and its normal form. Zürich: European Mathematical Society (EMS); 2014. (EMS series of lectures in mathematics).