Integrable quasiclassical deformations of algebraic curves

Journal of Physics A: Mathematical and General

Volumn 37, Issue 32, 2004, Pages 7859-7877

  Konopelchenko, B ^a   Alonso, L Martínez ^b  

^a UNIVERSITY OF SALENTO   (Italy)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4043150725     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/32/003     Document Type: Article

References (42)

1. Novikov S P, Manakov S V, Pitaevski L P and Zakharov V E 1984 Theory of solitons The Inverse Scattering Method (New York: Plenum)
2. Belokolos E D, Bobenko A I, Enol'ski V Z, Its A R and Matveev V B 1994 Algebra-Geometric Approach to Nonlinear Integrable Equations (Berlin: Springer)
3. Dubrovin B and Novikov S 1989 Russ. Math. Surv. 44 35
4. j and Segal-Wilson τ Function in Problems in Modern Quantum Field Theory ed A A Belavin, A V Klimyk and A B Zamolodchikov (Berlin: Springer)
5. Grinevich P G 1994 Nonisospectral Symmetries of the KdV Equation and the Corresponding Symmetries of the Whitham Equations in Singular Limits of Dispersive Waves (NATO ASI Series B; Physics vol 32) ed N M Ercolany et al (New York: Plenum)
6. Flaschka H, Forest M G and Mclauglin D W 1980 Commun. Pure Appl. Math. 33 739
7. Dubrovin B A 1992 Commun. Math. Phys. 145 415
8. Krichever I M 1988 Funct. Anal. Appl. 22 206
9. Krichever I M 1994 Commun. Pure. Appl. Math. 47 437
10. Krichever I M and Phong P H 1998 Simplectic Forms in the Theory of Solitons in Surveys in Differential Geometry IV ed G L Terng and K Uhlenbek (Hong Kong: International)
11. Kupershmidt B A 1990 J. Phys. A: Math. Gen. 23 871
12. Zakharov V E 1980 Funct. Anal. Appl. 14 15 Zakharov V E 1994 Dispersionless Limit of Integrable Systems in 2+1 Dimensions in Singular Limits of Dispersive Waves (NATO ASI Series B; Physics vol 32) ed N M Ercolany et al (New York: Plenum)
13. Zakharov V E 1980 Funct. Anal. Appl. 14 15 Zakharov V E 1994 Dispersionless Limit of Integrable Systems in 2+1 Dimensions in Singular Limits of Dispersive Waves (NATO ASI Series B; Physics vol 32) ed N M Ercolany et al (New York: Plenum)
14. Takasaki T and Takebe T 1992 Int. J. Mod. Phys. A 7 (Suppl. 1B) 889 Takasaki T and Takebe T 1995 Rev. Math. Phys. 7 743
15. Takasaki T and Takebe T 1992 Int. J. Mod. Phys. A 7 (Suppl. 1B) 889 Takasaki T and Takebe T 1995 Rev. Math. Phys. 7 743
16. Kodama Y 1988 Prog. Theor. Phys. Suppl. 95 184 Kodama Y 1988 Phys. Lett. A129 223
17. Kodama Y 1988 Prog. Theor. Phys. Suppl. 95 184 Kodama Y 1988 Phys. Lett. A129 223
18. Kodama Y and Gibbons J 1989 Phys. Lett. A 135 167
19. Mineev-Weinstein M, Wiegmann P B and Zabrodin A 2000 Phys. Rev. Lett. 84 5106
20. Fairlie D B and Strachan I A B 1996 Phys. D 90 1 Fairlie D B and Strachan I A B 1996 Inverse Probl. 12 885
21. Fairlie D B and Strachan I A B 1996 Phys. D 90 1 Fairlie D B and Strachan I A B 1996 Inverse Probl. 12 885
22. Strachan I A B 1999 J. Math. Phys. 40 5058
23. Kodama Y and Konopelchenko B G 2002 J. Phys. A: Math. Gen. 35 L489-L500 Kodama Y and Konopelchenko B G 2003 Deformations of Plane Algebraic Curves and Integrable Systems of Hydrodynamic Type in Nonlinear Physics: Theory and Experiment II ed M J Ablowitz et al (Singapore: World Scientific)
24. Kodama Y and Konopelchenko B G 2002 J. Phys. A: Math. Gen. 35 L489-L500 Kodama Y and Konopelchenko B G 2003 Deformations of Plane Algebraic Curves and Integrable Systems of Hydrodynamic Type in Nonlinear Physics: Theory and Experiment II ed M J Ablowitz et al (Singapore: World Scientific)
25. Ferapontov E V and Pavlov M V 1991 Phys. D 52 211
26. Gibbons J and Tsarev S P 1996 Phys. Lett. A 211 19 Gibbons J and Tsarev S P 1999 Phys. Lett. A 258 263
27. Gibbons J and Tsarev S P 1996 Phys. Lett. A 211 19 Gibbons J and Tsarev S P 1999 Phys. Lett. A 258 263
28. Mañas M, Martinez Alonso L and Medina E 2002 J. Phys. A: Math. Gen. 35 401
29. Kokotov A and Korotkin D 2004 A new hierarchy of integrable systems associated to Hurwitz spaces Preprint math-ph/0112051
30. Manas M, Martinez Alonso L and Medina E 1997 J. Phys. A: Math. Gen. 40 4815
31. Gelfand I M and Dikii L A 1976 Funkts. Anal. Prilozen. 10 13 Gelfand I M and Dikii L A 1977 Punkts. Anal. Prilozen. 11 11 Gelfand I M and Dikii L A 1978 Punkts. Anal. Prilozen. 12 8
32. Gelfand I M and Dikii L A 1976 Funkts. Anal. Prilozen. 10 13 Gelfand I M and Dikii L A 1977 Punkts. Anal. Prilozen. 11 11 Gelfand I M and Dikii L A 1978 Punkts. Anal. Prilozen. 12 8
33. Gelfand I M and Dikii L A 1976 Funkts. Anal. Prilozen. 10 13 Gelfand I M and Dikii L A 1977 Punkts. Anal. Prilozen. 11 11 Gelfand I M and Dikii L A 1978 Punkts. Anal. Prilozen. 12 8
34. Abhyankar S S 1990 Algebraic Geometry for Scientists and Engineers (Mathematical Surveys and Monograps vol 35) (Providence, RI: American Mathematical Society)
35. Walker R Y 1978 Algebraic Curves (Berlin: Springer)
36. Farkas H M and Kra I 1980 Riemann Surfaces (Berlin: Springer)
37. Kostrikin A I 1982 Introduction to Algebra (Berlin: Springer)
38. Macdonald I G 1979 Symmetric Functions and Hall Polynomials (Oxford: Clarendon)
39. Konopelchenko B G and Dubrosky V G 1984 Ann. Phys. 156 265
40. Kurosh A G 1972 Higher Algebra (Moscow: Mir)
41. Reyman A G and Semenov-Tian-shansky M A 1988 Phys. Lett. A 130 456
42. Fordy A P, Reyman A G and Semenov-Tian-shansky M A 1989 Lett. Math. Phys. 17 25