Hyperelliptic solutions of KdV and KP equations: Re-evaluation of Baker's study on hyperelliptic sigma functions

Journal of Physics A: Mathematical and General

Volumn 34, Issue 22, 2001, Pages 4721-4732

  Matsutani, Shigeki ^a  

^a NONE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035827486     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/22/312     Document Type: Article

References (25)

1. Baker H F 1897 Abelian Functions - Abel's Theorem and the Allied Theory Including the Theory of the Theta Functions (Cambridge: Cambridge University Press) republication 1995
2. Baker H F 1898 On the hyperelliptic sigma functions Am. J. Math. 20 301-84
3. Baker H F 1903 On a system of differential equations leading to periodic functions Acta Math. 27 135-56
4. Buchstaber V M, Enolskii V Z and Leykin D V 1997 Hyperelliptic Kleinian functions and application Am. Math. Soc. Transl. 179 1-33
5. Buchstaber V M, Enolskii V Z and Leykin DV 1997 Kleinian functions, hyperelliptic Jacobians and applications Reviews in Mathematics and Mathematical Physics (London) ed S P Novikov and IM Krichever (India: Gordon and Breach) pp 1-125
6. Buchstaber V M, Enolskii V Z and Leykin D V 2000 Uniformization of the Jacobi varieties of trigonal curves and nonlinear differential equations Funct. Anal. Appl. 34 1-15
7. Christiansen P L, Eilbeck J C, Enolskii V Z and Rostov N A 2000 Quasi-periodic and periodic solutions for coupled nonlinear Schrödinger equations of Manakov type Proc. R. Soc. A 456 2263-81
8. Date E, Kashiwara M, Jimbo M and Miwa T 1983 Transformation groups for soliton equations Nonlinear Integrable Systems - Classical Theory and Quantum Theory ed M Jimbo and T Miwa (Singapore: World Scientific) pp 39-119
9. Eilbeck J C and Enolskii V Z 2000 Bilinear operators and the power series for the Weierstrass σ function J. Phys. A: Math. Gen. 33 791-4
10. Eilbeck J C, Enolskii V Z and Leykin D V 2000 On the Kleinian construction of Abelian functions of canonical algebraic curves Proc. Conf. SIDE III: Symmetries of Integrable Differences Equations (Saubadia, May 1998) (CRM Proceedings and Lecture Notes) pp 121-38
11. Eilbeck J C, Enolskii V Z and Perviato E 2000 Varieties of elliptic solitons J. Phys. A: Math. Gen. 456 2263-81
12. Grant D 1990 Formal groups in genus two J. Reine Ang. Math. 411 96-121
13. Hirota R 1976 Direct method of finding exact solutions of nonlinear evolution equations Bäcklund Transformations (Lecture Notes in Math. vol 515) ed R M Miura (Berlin: Springer)
14. Hirota R and Ito M 1981 A direct approach to multi-periodic wave solutions to nonlinear evolution equations J. Phys. Soc. Japan 50 338-42
15. Krichever I M 1977 Methods of algebraic geometry in the theory of nonlinear equations Russ. Math. Surv. 32 185-213
16. Krichever I M Foreword in the republication of [B1]
17. Kawamoto N, Namikawa Y, Tsuchiya A and Yamada Y 1988 Geometric realization of conformal field theory on Riemannian surfaces Commun. Math. Phys. 116 247-308
18. Mumford D 1984 Tata Lectures on Theta II (Prog. in Math. vol 43) (Basle: Birkhäuser)
19. Matsutani S 1998 Statistical mechanics of elastica on plane: origin of MKdV hierarchy J. Phys. A: Math. Gen. 31 2705-25
20. Matsutani S 2001 Closed loop solitons and sigma functions: classical and quantized elasticas with genera one and two J. Geom. Phys. 698
21. Nijhoff F W 2000 Discrete Dubrovin equations and separation of variables for discrete systems Chaos Solitons Fractals 11 19-28
22. Ônishi Y 1998 Complex multiplication formulae for curves of genus three Tokyo J. Math. 21 381-431
23. Ônishi Y 1998 Chodaenkansuu-ron Introduction to Hyperelliptic Function (in Japanese) unpublished
24. Ônishi Y 2000 Determinatal expressions for some Abelian functions in genus two Preprint
25. Sato M and Sato Y 1984 Soliton equations as dynamics systems on infinite dimensional Grassmann manifold Nonlinear Partial Differential Equations in Applied Science ed H Fujita, P D Lax and G Strang (Tokyo: Kinokuniya/North-Holland)