Geodesic
Nondegeneracy of amplitude-frequency modulation for finite-gap solutions of integrable nonlinear equations
Matematičeskie zametki, Tome 59 (1996) no. 1, pp. 53-61.

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We study properties of complex finite-gap solutions of the nonlinear Schrödinger equation and the sine-Gordon model. 
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R. F. Bikbaev. Nondegeneracy of amplitude-frequency modulation for finite-gap solutions of integrable nonlinear equations. Matematičeskie zametki, Tome 59 (1996) no. 1, pp. 53-61. http://geodesic.mathdoc.fr/item/MZM_1996_59_1_a4/

[1] Krichever I. M., “Perturbation theory in periodic problems for two-dimensional integrable systems”, Sov. Sci. Rev. C. Math. Phys., 9 (1991), 1–101

[2] Bikbaev R. F., Kuksin S. B., “On the parametrization of finite-gap solutions by the frequency and wave number vectors and a Theorem of I. Krichever”, Lett. Math. Phys., 28 (1993), 115–122 | DOI | MR | Zbl

[3] Bikbaev R. F., “Algebro-geometricheskie neravenstva, porozhdaemye teoriei vozmuschenii: nelineinye uravneniya Shredingera”, Algebra i analiz, 5:4 (1993), 67–82 | MR

[4] Bikbaev R. F., Kuksin S. B., “Periodicheskaya kraevaya zadacha dlya uravneniya Sinus–Gordon, ee malye gamiltonovy vozmuscheniya i KAM-deformatsii konechnozonnykh torov”, Algebra i analiz, 4:3 (1992), 42–78 | MR