Solving the dispersionless Dym equation by hodograph transformations

Journal of Physics A: Mathematical and General

Volumn 36, Issue 38, 2003, Pages 9875-9883

  Chen, Yu Tung ^a   Tu, Ming Hsien ^a  

^a NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142198844     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/38/305     Document Type: Article

References (20)

1. Takasaki K and Takebe T 1995 Integrable hierarchies and dispersionless limit Rev. Math. Phys. 7 743-808
2. Dijkgraaf R and Witten E 1990 Mean field theory, topological field theory, and multi-matrix models Nucl. Phys. B 342 486-522
3. Krichever I 1992 The dispersionless Lax equations and topological minimal models Commun. Math. Phys. 143 415-29
4. Dubrovin B 1996 Geometry of 2D topological field theories Integrable Systems and Quantum Group ed M Francaviglia and S Greco (Berlin: Springer) pp 120-348
5. 1 model and the laigt-N matrix integral Mod. Phys. Lett. A 9 2893-902
6. Aoyama S and Kodama Y 1994 Topological conformal field theory with a rational W potential and the dispersionless KP hierarchy Mod. Phys. Lett. A 9 2481-91 Aoyama S and Kodama Y 1996 Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy Commun. Math. Phys. 182 185-219
7. Aoyama S and Kodama Y 1994 Topological conformal field theory with a rational W potential and the dispersionless KP hierarchy Mod. Phys. Lett. A 9 2481-91 Aoyama S and Kodama Y 1996 Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy Commun. Math. Phys. 182 185-219
8. Wiegmann P B and Zabrodin A 2000 Conformal maps and integrable hierarchies Commun. Math. Phys. 213 523-38
9. Kodama Y 1988 A method for solving the dispersionless KP equation and its exact solutions Phys. Lett. A 129 223-6
10. Kodama Y and Gibbons J 1989 A method for solving the dispersionless KP hierarchy and its exact solutions: II Phys. Lett. A 135 167-70
11. Tsarev S P 1985 On Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type Sov. Math. Dokl. 31 488-91
12. Dubrovin B and Novikov S P 1984 Poisson brackets of hydrodynamic type Sov. Math. Dokl. 30 651-4
13. Li L C 1999 Classical r-matrices and compatible Poisson structures for Lax equations on Poisson algebras Commun. Math. Phys. 203 573-92
14. Blaszak M and Szablikowski B M 2002 Classical R-matrices theory of dispersionless systems: I (1+1)dimension theory J. Phys. A: Math. Gen. 35 10325-44
15. Chen Y T and Tu M H 2003 A note on the dispersionless Dym hierarchy Lett. Math. Phys. 63 125-39
16. Aratyn H, Nissimov E, Pacheva S and Vaysburd 11992 R-matrix formulation of KP hierarchies and their gauge equivalence Phys. Lett. B 294 167-76
17. Konopelchenko B and Oevel W 1993 An r-matrix approach to nonstandard classes of integrable equations Publ. Res. Inst Math. Sci. 29 581-666
18. Konopelchenko B G and Dubrovsky V G 1984 Some new integrable nonlinear evolution equations in 2 + 1 dimensions Phys. Lett. A 102 15-7
19. Kupershmidt B A and Manin Y I 1977 Long wave equations with a free surface: I. Conservation laws and solutions Funct. Anal. Phys. 11 31-42 Kupershmidt B A and Manin Y I 1978 Long wave equations with a free surface: II. The Hamiltonian structure and the higher equations Funct. Anal. Phys. 12 25-37
20. Kupershmidt B A and Manin Y I 1977 Long wave equations with a free surface: I. Conservation laws and solutions Funct. Anal. Phys. 11 31-42 Kupershmidt B A and Manin Y I 1978 Long wave equations with a free surface: II. The Hamiltonian structure and the higher equations Funct. Anal. Phys. 12 25-37