Dressing Chains and Spectral Theory of the Schr\"odinger Operator
Funkcionalʹnyj analiz i ego priloženiâ, Tome 27 (1993) no. 2, pp. 1-21.

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A. P. Veselov; A. B. Shabat. Dressing Chains and Spectral Theory of the Schr\"odinger Operator. Funkcionalʹnyj analiz i ego priloženiâ, Tome 27 (1993) no. 2, pp. 1-21. http://geodesic.mathdoc.fr/item/FAA_1993_27_2_a0/

[1] Novikov S. P., “Periodicheskaya zadacha dlya uravneniya Kortevega–de Friza, I”, Funkts. analiz i ego pril., 8:3 (1974), 54–66 | MR | Zbl

[2] Dubrovin B. A., Matveev V. B., Novikov S. P., “Nelineinye uravneniya tipa Kortevega–de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, UMN, 31:1 (1976), 55–136 | MR | Zbl

[3] Lax P. D., “Periodic solutions of Korteweg–de Vries equation”, Comm. Pure Appl. Math., 28 (1975), 141–188 | DOI | MR | Zbl

[4] McKean H. P., van Moerbeke P., “The spectrum of Hill's equation”, Invent. Math., 30 (1975), 217–274 | DOI | MR | Zbl

[5] Marchenko V. A., Operatory Shturma–Liuvillya i ikh prilozheniya, Naukova dumka, Kiev, 1977 | MR

[6] Darboux G., “Sur la representations spherique des surfaces”, Compt. Rend., 94 (1882), 1343–1345

[7] Crum M. M., “Associated Sturm–Liouville systems”, Quart. J. Math. Ser. 2, 6 (1955), 121–127 | DOI | MR

[8] Shabat A. B., “Odnomernye vozmuscheniya differentsialnykh operatorov i obratnaya zadacha rasseyaniya”, Zadachi mekhaniki i matematicheskoi fiziki, Nauka, M., 1976, 279–294

[9] Deift P., “Application of a commutation formula”, Duke Math. J., 45 (1978), 267–310 | DOI | MR | Zbl

[10] Adler M., Moser J., “On a class of polynomials connected with the Korteweg–de Vries equation”, Comm. Math. Phys., 61 (1978), 1–30 | DOI | MR | Zbl

[11] Shabat A. B., “The infinite-dimensional dressing dynamical system”, Inverse Problems, 6 (1992), 303–308 | DOI | MR

[12] Shabat A. B., Yamilov R. I., “Simmetrii nelineinykh tsepochek”, Algebra i analiz, 2:2 (1990), 183–208 | MR

[13] Veselov A. P., “O gamiltonovom formalizme dlya uravnenii Novikova–Krichevera kommutativnosti dvukh operatorov”, Funkts. analiz i ego pril., 13:1 (1979), 1–7 | MR | Zbl

[14] Burchnall J. L., Chaundy T. W., “Commutative ordinary differential operators”, Proc. London Soc. Ser. 2, 21 (1923), 420–440 | DOI | MR | Zbl

[15] Ains E. L., Obyknovennye differentsialnye uravneniya, ONTI, Kharkov, 1939

[16] Magri F., “A simple model of integrable Hamiltonian equation”, J. Math. Phys., 19 (1978), 1156–1162 | DOI | MR | Zbl

[17] Gelfand I. M., Dorfman I. Ya., “Gamiltonovy operatory i svyazannye s nimi algebraicheskie struktury”, Funkts. analiz i ego pril., 13:4 (1979), 13–30 | MR

[18] Antonowicz M., Fordy A. P., Wojciechowski S., “Integrable stationary flows: Miura maps and bi-Hamiltonian structures”, Phys. Lett. A., 124 (1987), 143–150 | DOI | MR

[19] Weiss J., “Periodic fixed points of Backlund transformations and the KdV equation”, J. Math. Phys., 27(11) (1986), 2647–2656 ; 28(9) (1987), 2025–2039 | DOI | MR | Zbl | DOI | MR | Zbl

[20] Santini P., “Solvable nonlinear algebraic equations”, Inverse Problems, 6 (1990) | DOI | MR

[21] Veselov A. P., “O roste chisla obrazov tochki pri iteratsiyakh mnogoznachnogo otobrazheniya”, Mat. zametki, 49:2 (1991), 29–35 | MR | Zbl

[22] Adler M., van Moerbeke P., “Algebraic integrable systems: a systematic approach”, Perspectives in Math., Acad. Press, Boston, 1989 | MR | Zbl

[23] Adler V. E., “Perekroika mnogougolnikov”, Funkts. analiz i ego pril., 27:2 (1993), 79–82 | MR | Zbl

[24] Bureau F. J., “Integration of some nonlinear systems of ordinary differential equations”, Annali di Mat. Pura Appl. (IV), 44 (1972), 345–360 | DOI | MR

[25] Ehlers F., Knorrer H., “An algebro-geometric interpretation of the Backlund transformation for the Korteweg–de Vries equation”, Comm. Math. Helv., 57:1 (1982), 1–10 | DOI | MR | Zbl

[26] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. 3, Nauka, M., 1967 | MR

[27] S. P. Novikov (red.), Teoriya solitonov, Nauka, M., 1980 | MR

[28] McKean H. P., Trubowitz E., “The spectral class of the quantum mechanical harmonic oscillator”, Comm. Math. Phys., 82 (1982), 471–495 | DOI | MR | Zbl

[29] Levitan B. M., “Ob operatorakh Shturma–Liuvillya na vsei pryamoi s odinakovym spektrom”, Mat. sbornik, 132:1 (1987), 73–103 | MR | Zbl