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Monodromy- and spectrum-preserving deformations. I. (English) Zbl 0439.34005


MSC:

34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
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[1] Ince, E.L.: Ordinary differential equations. New York: Dover Publications 1947 · Zbl 0063.02971
[2] Ablowitz, M.J., Segur, H.: Phys. Rev. Lett.38, 1103-1106 (1977)
[3] Airault, H.: Rational solutions of Painlevé equations (to appear) · Zbl 0496.58012
[4] Wu, T.T., McCoy, B.M., Tracy, C.A., Barouch, E.: Phys. Rev. B13, 316-371 (1976)
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[6] McCoy, B.M., Tracy, C.A., Wu, T.T.: J. Math. Phys.18, 1058-1092 (1977) · Zbl 0353.33008
[7] Sat?, M., Miwa, T., Jimbo, M.: A series of papers entitled Holonomic Quantum Fields: I. Publ. RIMS, Kyoto Univ.14, 223-267 (1977); II. Publ. RIMS, Kyoto Univ.15, 201-278 (1979); III. Publ. RIMS Kyoto Univ.15, 577-629 (1979). IV., V. RIMS Preprints 263 (1978), and 267 (1978). The paper we refer to most often is III. See also a series of short notes: Studies on holonomic quantum fields, I?XV · Zbl 0383.35066
[8] Gardner, C.S., Greene, J.M., Kruskal, M.D., Miura, R.M.: Commun. Pure Appl. Math.27, 97-133 (1976) · Zbl 0291.35012
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[10] Ablowitz, M.J., Segur, H.: Stud. Appl. Math.57, 13-44 (1977)
[11] Hastings, S.P., McLeod, J.B.: Univ. of Wisconsin, MRC Report No. 1861 (1978)
[12] Ablowitz, M.J., Ramani, A., Segur, H.: Lett. Nuovo Cimento23, 333 (1978).
[13] Two preprints: A connection between nonlinear evolution equations and ordinary differential equations ofP-type, I, II
[14] Tracy, C.A.: Proc. NATO Advanced Study Institute on: Nonlinear equations in physics and mathematics, 1978, (ed. A. Barut). Dordrecht, Holland: Reidel 1978
[15] Schlesinger, L.: J. Reine Angewandte Math.141, 96-145 (1912) · JFM 43.0385.01
[16] Garnier, R.: Ann. Ec. Norm. Sup.29, 1-126 (1912) · JFM 43.0382.01
[17] Birkhoff, G.D.: Trans. AMS10, 436-470 (1909) · JFM 40.0352.02
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[19] Garnier, R.: Rend. Circ. Mat. Palermo,43, 155-191 (1919) · JFM 47.0404.01
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[22] Moser, J., Trubowitz, E.: (to appear)
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[24] Ablowitz, M.J., Kaup, D.J., Newell, A.C., Segur, H.: Stud. Appl. Math.53, 249-315 (1974)
[25] Flaschka, H., Newell, A.C.: Springer Lecture Notes in Physics38, 355-440 (1975)
[26] Airault, H., McKean, Jr., H.P., Moser, J.: Comm. Pure Appl. Math.30, 95-148 (1977) · Zbl 0338.35024
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[28] Ueno, K.: Kyoto, RIMS master’s thesis, Dec. 1978. RIMS Preprints 301, 302 (1979)
[29] Sibuya, Y.: Proc. Int. Conf. Diff. Eq. pp. 709-738. (ed. H. A. Antosiewicz). New York: Academic Press 1975;
[30] Bull. AMS83, 1075-1077 (1977) · Zbl 0386.34008
[31] Zakharov, V.E., Shabat, A.B.: Sov. Phys. JETP34, 62-69 (1972)
[32] Zakharov, V.E.: Paper at I. G. Petrovskii Memorial Converence, Moscow State Univ., Jan. 1976 (this paper has been referred to in many subsequent publications, but has apparently never been published)
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[34] Novikov, S.P.: Rocky Mt. J. Math.8, 83-94 (1978) · Zbl 0436.35071
[35] Newell, A.C.: Proc. Roy. Soc. London A365, 283-311 (1979) · Zbl 0403.35048
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