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

MSC:
34M55Painlevé and other special equations; classification, hierarchies
References:
[1]Ince, E.L.: Ordinary differential equations. New York: Dover Publications 1947
[2]Ablowitz, M.J., Segur, H.: Phys. Rev. Lett.38, 1103-1106 (1977) · doi:10.1103/PhysRevLett.38.1103
[3]Airault, H.: Rational solutions of Painlevé equations (to appear)
[4]Wu, T.T., McCoy, B.M., Tracy, C.A., Barouch, E.: Phys. Rev. B13, 316-371 (1976) · doi:10.1103/PhysRevB.13.316
[5]Barouch, E., McCoy, B.M., Wu, T.T.: Phys. Rev. Lett.31, 1409-1411 (1973) · doi:10.1103/PhysRevLett.31.1409
[6]McCoy, B.M., Tracy, C.A., Wu, T.T.: J. Math. Phys.18, 1058-1092 (1977) · Zbl 0353.33008 · doi:10.1063/1.523367
[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 · doi:10.2977/prims/1195189284
[8]Gardner, C.S., Greene, J.M., Kruskal, M.D., Miura, R.M.: Commun. Pure Appl. Math.27, 97-133 (1976) · Zbl 0291.35012 · doi:10.1002/cpa.3160270108
[9]Fuchs, R.: Math. Ann.63, 301-321 (1906) · Zbl 02644002 · doi:10.1007/BF01449199
[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). · doi:10.1007/BF02824479
[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) · Zbl 02625645 · doi:10.1515/crll.1912.141.96
[16]Garnier, R.: Ann. Ec. Norm. Sup.29, 1-126 (1912)
[17]Birkhoff, G.D.: Trans. AMS10, 436-470 (1909) · doi:10.1090/S0002-9947-1909-1500848-5
[18]Birkhoff, G.D.: Proc. Am. Acad. Arts Sci.49, 521-568 (1913) · doi:10.2307/20025482
[19]Garnier, R.: Rend. Circ. Mat. Palermo,43, 155-191 (1919) · Zbl 02606754 · doi:10.1007/BF03014668
[20]Davis, H.T.: Introduction to nonlinear differential and integral equations. New York: Dover Publications 1962
[21]Choodnovsky, D.V., Choodnovsky, G.V.: Completely integrable class of mechanical systems connected with Korteweg-deVries and multicomponent Schrödinger equations. I. Preprint, École Polytechnique, 1978
[22]Moser, J., Trubowitz, E.: (to appear)
[23]Olver, F.W.J.: Asymptotics and special functions. New York: Academic Press 1974
[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) · doi:10.1007/3-540-07171-7_10
[26]Airault, H., McKean, Jr., H.P., Moser, J.: Comm. Pure Appl. Math.30, 95-148 (1977) · Zbl 0338.35024 · doi:10.1002/cpa.3160300106
[27]Brieskorn, E.: Jber. Dt. Math.-Verein.78, 93-112 (1976)
[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 · doi:10.1090/S0002-9904-1977-14391-7
[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)
[33]Krichever, I.M.: Funkts. Anal. Prilozen11, 15-31 (1977)
[34]Novikov, S.P.: Rocky Mt. J. Math.8, 83-94 (1978) · Zbl 0436.35071 · doi:10.1216/RMJ-1978-8-1-83
[35]Newell, A.C.: Proc. Roy. Soc. London A365, 283-311 (1979) · Zbl 0403.35048 · doi:10.1098/rspa.1979.0018