Varieties of elliptic solitons

Journal of Physics A: Mathematical and General

Volumn 34, Issue 11, 2001, Pages 2215-2227

  Eilbeck, J C ^a   Enolskii, V Z ^a,b   Previato, E ^c  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b INSTITUTE OF MAGNETISM   (Ukraine)

^c USA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035937694     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/11/314     Document Type: Article

References (30)

1. Airault H, McKean H P and Moser J 1977 Rational and elliptic solutions of the KdV equation and a related many-body problem Commun. Pure Appl. Math. 30 94-148
2. Bateman H and Erdelyi A 1955 Higher Transcendental Functions vol 2 (New York: McGraw-Hill)
3. Belokolos E D, Bobenko A I, Enolskii V Z, Its A R and Matveev V B 1994 Algebro Geometrical Approach to Nonlinear Integrable Equations (Berlin: Springer)
4. Belokolos E D and Enolskii V Z 2000 Reduction of Abelian Functions and Algebraically Integrable Systems parts I and II (J. Math. Sci., Viniti, Plenum) at press
5. Buchstaber V M, Enolskii V Z and Leykin D V 1997 Kleinian functions, hyperelliptic Jacobians and applications Reviews in Mathematics and Mathematical Physics vol 10:2, ed S P Novikov and I M Krichever (London: Gordon and Breach) pp 1-125
6. Buchstaber V M, Enolskii V Z and Leykin D V 1999 Rational analogues of the Abelian functions Fund. Anal. Appl. 33 83-94
7. Buchstaber V M, Enolskii V Z and Leykin D V 2000 Uniformisation of Jacobi varieties of trigonal curves and nonlinear differential equations Funct. Anal. Appl. 34 1-15
8. Burchnall J L and Chaundy T W 1928 Commutative ordinary differential operators. I Proc. Lond. Math. Soc. 118 420-40
9. Burchnall J L and Chaundy T W 1928 Commutative ordinary differential operators. II Proc. Lond. Math. Soc. 118 557-83
10. Cox D, Little L and O'Shea D 1992 Ideals, Varieties, and Algorithms (Berlin: Springer)
11. Dickson R, Gesztesy F and Unterkofler K 1999 Algebro-geometric solutions of the Boussinesq hierarchy Rev. Mod. Phys. 11 823-79
12. Dickson R, Gesztesy P and Unterkofler K 1999 A new approach to the Boussinesq hierarchy Math. Nachr. 198 51-108
13. Dubrovin B A and Novikov S P 1974 Periodic and quasiperiodic analogues of multisoliton solutions of Korteweg-de Vries equation Sov. Phys.-JETP 67 2131-43
14. Eilbeck J C, Enolskii V Z and Leykin D V 2000 On the Kleinian construction of Abelian functions of canonical algebraic curve Proc. Conf. SIDE III: Symmetries of Integrable Differences Equations (Saubadia, 1998) (CRM Proc. Lecture Notes vol 25) pp 121-38
15. Enolskii V Z 1984 On the solutions in elliptic functions of integrable non-linear equations connected with two-gap Lamé potentials Dokl. Akad. Nauk SSSR 278 305-9
16. Enolskii V Z and Eilbeck J C 1995 On the two-gap locus for the elliptic Calogero-Moser model J. Phys. A: Math. Gen. 28 1069-88
17. Enolskii V Z and Kostov N A 1994 On the geometry of elliptic solitons Acta Appl. Math. 36 57-86
18. Gavrilov L and Perelomov A M 1999 On explicit solution of Calogero-Moser system J. Math. Phys. 40 6339-52
19. Halphen G H 1884 Mémoire sur la réduction des équations différentielles linéaires aux formes intégrales Mem. Prés. Acad Sci. France 28 1-300
20. Hermite C 1912 Oeuvres de Charles Hermite vol 3 (Paris: Gauthier-Villars)
21. Kamke E 1959 Differentialgleichungen Lösungsmethoden und Lösungen. I. Gewohnliche Differentialgleichungen (Leipzig)
22. Klein F 1888 Über hyperelliptische Sigmafunctionen Math. Ann. 32 351-80
23. Krazer A 1903 Lehrbuch der Thetafunktionen (Leipzig: Teubner)
24. Krichever I M 1980 Elliptic solutions of Kadomtsev-Petviashvili equation and integrable particle systems Funct. Anal. Appl. 14 45-54
25. Previato E 1994 Monodromy of Boussinesq elliptic operators Acta Appl. Math. 36 49-55
26. Previato E 1996 Seventy years of spectral curves: 1923-1993 Integrable systems and quantum groups (Montecatini Terme, 1993) (Lecture Notes in Mathematics vol 1620) (Berlin: Springer) pp 419-81
27. Treibich A and Verdier J L 1990 Solitons elliptiques Prog. Math. 88 (The Grothendieck Festschrift vol 3) (Boston, MA: Birkhäuser) pp 437-80
28. Treibich A and Verdier J L 1993 Variétés de Kritchever des solitons elliptiques de KP Proc. Indo-French Conf. on Geometry (Bombay, 1989) (Delhi: Hindustan) pp 187-232
29. Unterkofler K 2000 On the solutions of Halphen's equation Differential Integral Equations
30. Verdier J L 1990 New elliptic solitons Algebraic Analysis, Special Volume for 60th Anniversary of Professor M Sato ed M Kashiwara and T Kawai (New York: Academic) pp 901-10