Hyperelliptic Riemann surfaces of infinite genus and solutions of the KdV equation
W. Müller, M. Schmidt, and R. Schrader
Source: Duke Math. J. Volume 91, Number 2
(1998), 315-352.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077232081
Mathematical Reviews number (MathSciNet): MR1600590
Zentralblatt MATH identifier: 0962.35151
Digital Object Identifier: doi:10.1215/S0012-7094-98-09114-1
References
[1] R. D. M. Accola, The bilinear relation on open Riemann surfaces, Trans. Amer. Math. Soc. 96 (1960), 143–161.
Mathematical Reviews (MathSciNet): MR23:A2521
Zentralblatt MATH: 0118.30003
Digital Object Identifier: doi:10.2307/1993490
JSTOR: links.jstor.org
[2] E. D. Belokolos, et al., Algebro-Geometric Approach to Nonlinear Integrable Equations, Springer Ser. Nonlinear Dynam., Springer-Verlag, Berlin, 1994.
Zentralblatt MATH: 0809.35001
[3] H. Bohr, Almost Periodic Functions, Chelsea Publishing Company, New York, N.Y., 1947.
Mathematical Reviews (MathSciNet): MR8,512a
[4] B. Dubrovin, I. Krichever, and S. P. Novikov, Integrable systems, I, Dynamical Systems, IV, Encyclopaedia of Math. Sci., vol. 4, Springer-Verlag, Berlin, 1990, pp. 173–280.
Zentralblatt MATH: 0780.58019
[5] B. Dubrovin, V. B. Matveev, and S. P. Novikov, Non-linear equations of Korteweg-de Vries type, finite-zone linear operators, and abelian varieties, Russian Math. Surveys 31 (1976), 59–136.
Zentralblatt MATH: 0346.35025
Mathematical Reviews (MathSciNet): MR427869
[6] J. D. Fay, Theta functions on Riemann surfaces, Lecture Notes in Math., Springer-Verlag, Berlin, 1973.
Mathematical Reviews (MathSciNet): MR49:569
Zentralblatt MATH: 0281.30013
[7] J. Feldman, H. Knörrer, and E. Trubowitz, Riemann surfaces of infinite genus, I: $L^2$-cohomology, exhaustions with finite charge and theta series, preprint, FIM-ETH, 1994.
[8] A. R. Its and V. B. Matveev, Schrödinger operators with the finite-band spectrum and the $N$-soliton solutions of the Korteweg-de Vries equation, Teoret. Mat. Fiz. 23 (1975), no. 1, 51–68.
Mathematical Reviews (MathSciNet): MR57:18570
[9] S. Lang, Elliptic functions, Graduate Texts in Mathematics, vol. 112, Springer-Verlag, New York, 1987.
Mathematical Reviews (MathSciNet): MR88c:11028
Zentralblatt MATH: 0615.14018
[10] P. D. Lax, Periodic solutions of the KdV equation, Comm. Pure Appl. Math. 28 (1975), 141–188.
Mathematical Reviews (MathSciNet): MR51:6192
Zentralblatt MATH: 0295.35004
[11] B. M. Levitan, Almost periodicity of infinite-zone potentials, Math. USSR-Izv. 18 (1982), 249–273.
Zentralblatt MATH: 0483.35075
[12] V. B. Matveev, A new method of integrating the Korteweg-de Vries equation, Uspekhi Mat. Nauk 30 (1975), 201–203 (in Russian).
[13] H. P. McKean and P. van Moerbeke, The spectrum of Hill's equation, Invent. Math. 30 (1975), no. 3, 217–274.
Mathematical Reviews (MathSciNet): MR53:936
Zentralblatt MATH: 0319.34024
Digital Object Identifier: doi:10.1007/BF01425567
[14] H. McKean and E. Trubowitz, Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points, Comm. Pure Appl. Math. 29 (1976), no. 2, 143–226.
Mathematical Reviews (MathSciNet): MR55:761
Zentralblatt MATH: 0339.34024
Digital Object Identifier: doi:10.1002/cpa.3160290203
[15] H. McKean and E. Trubowitz, Hill's surfaces and their theta functions, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1042–1085.
Mathematical Reviews (MathSciNet): MR80b:30039
Zentralblatt MATH: 0428.34026
Digital Object Identifier: doi:10.1090/S0002-9904-1978-14542-X
Project Euclid: euclid.bams/1183541462
[16] W. Müller, M. Schmidt, and R. Schrader, Theta functions for infinite period matrices, Internat. Math. Res. Notices (1996), no. 12, 565–587.
Mathematical Reviews (MathSciNet): MR99a:14071
Zentralblatt MATH: 0872.14038
[17] S. P. Novikov, The periodic problem for the Korteweg-de Vries equation, I, Functional Anal. Appl. 8 (1974), 236–246.
Zentralblatt MATH: 0299.35017
Mathematical Reviews (MathSciNet): MR382878
[18] M. Schmidt, Integrable systems and Riemann surfaces of infinite genus, Mem. Amer. Math. Soc. 122 (1996), no. 581, viii+111.
Mathematical Reviews (MathSciNet): MR96k:58123
Zentralblatt MATH: 0867.58038
[19] K. Tahara, On the hyperelliptic Riemann surfaces of infinite genus with absolutely convergent Riemann's theta functions, Nagoya Math. J. 33 (1968), 57–73.
Mathematical Reviews (MathSciNet): MR38:3427
Zentralblatt MATH: 0167.19102
Project Euclid: euclid.nmj/1118797589
Duke Mathematical Journal
