The (2+1)-dimensional nonisospectral relativistic Toda hierarchy related to the generalized discrete Painlevé hierarchy

Journal of Physics A: Mathematical and Theoretical

Volumn 40, Issue 27, 2007, Pages 7707-7719

  Zhu, Zuo Nong ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34250716329     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/40/27/019     Document Type: Article

References (34)

1. Ruijsenaars S N M 1990 Relativistic Toda lattice Commun. Math. Phys. 133 217
2. Bruschi M and Ragnisco O 1988 Recurision operator and Bäcklund transformation for the Ruijsenaars-Toda lattice Phys. Lett. A 129 21-5
3. Bruschi M and Ragnisco O 1989 Lax representation and complete integrability for the periodic relativistic Toda lattice Phys. Lett. A 134 365-70
4. Ragnisco O and Bruschi M 1989 The periodic relativistic Toda lattice: direct and inverse problem Inverse Problems 5 389-406
5. Suris Y B 1990 Discrete-time generalized Toda lattices: complete integrability and relation with relativistic Toda lattices Phys. Lett. A 145 113-9
6. Suris Y B 1993 On the bi-hamiltonian structures of Toda and relativistic Toda lattices Phys. Lett. A 180 419-29
7. Kadomtsev B B and Petviashvili V I 1970 On the stability of solitary waves in weakly dispersing media Sov. Phys.-Dokl. 15 539-41
8. Mason L J and Newman E T 1989 A connection between the Einstein and Yang-Mills equations Commun. Math. Phys. 121 659-68
9. Donaldson S K 1983 An application of gauge theory to the topology of 4-fanifolds J. Diff. Geom. 18 269-316
10. Rajaraman R 1989 Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory (Amsterdam: North-Holland)
11. Manakov S V and Zakharov V E 1981 Three-dimensional model of relativistic-invariant field theory, integrable by the inverse scattering transform Lett. Math. Phys. 5 247-53
12. Ablowitz M J, Chakravarty S and Takhtajan L A 1993 A self-dual Yang-Mills hierarchy and its reductions to integrable systems in 1+1 and 2+1 dimensions Commun. Math. Phys. 158 289-314
13. Ablowitz M J, Chakravarty S and Halburd R G 2003 Integrable systems and reductions of the self-dual Yang-Mills equations J. Math. Phys. 44 3147-73
14. Mikhailov A V 1981 The reduction problem and the inverse scattering method Physica D 3 73-117
15. Villarroel J, Chakravarty S and Ablowitz M J 1996 On a 2+1 Volterra system Nonlinearity 9 1113-28
16. Date E, Jinbo M and Miwa T 1982 Method for generating discrete soliton equations: I J. Phys. Soc. Japan 51 4116
17. Blaszak M and Szum 2001 Lie algebraic approach to the construction of (2+1)-dimensional lattice-field and field integrable Hamiltonian equations J. Math. Phys. 42 225
18. Calogero F 1975 A method to generate solvable nonlinear evolution equations Lett. Nuovo Cimento 14 443-7
19. Levi D and Ragnisco O 1979 Nonlinear differential-difference equations with N-dependent coefficients: I J. Phys. A: Math. Gen. 12 L157-62
20. Levi D and Ragnisco O 1979 Nonlinear differential-difference equations with N-dependent coefficients: II J. Phys. A: Math. Gen. 12 L163-L167
21. Bruschi M and Ragnisco O 1981 Nonlinear differential-difference matrix equations with N-dependent coefficients Lett. Nuovo Cimento 31 492-6
22. Ma W X and Fuchssteiner B 1999 Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations J. Math. Phys. 40 2400-18
23. Zhu Z N and Xue W M 2004 Two new integrable lattice hierarchies associated with a discrete Schrödinger nonisospectral problem and their infinitely many conservation laws Phys. Lett. A 320 396-407
24. Zhu Z N and Tam H W 2004 Nonisospectral negative Volterra flows and mixed Volterra flows: Lax pairs, infinitely many conservation laws and integrable time discretization J. Phys. A: Math. Gen. 37 3175-87
25. Gordoa P R, Pickering A and Zhu Z N 2005 A nonisospectral extension of the Volterra hierarchy to 2+1 dimensions J. Math. Phys. 46 103509
26. Gordoa P R, Pickering A and Zhu Z N 2006 A 2+1 non-isospectral integrable lattice hierarchy related to a generalized discrete second Painlevé hierarchy Chaos Solitons Fractals 29 862-70
27. Gordoa P R, Pickering A and Zhu Z N 2007 New 2+1 dimensional nonisospectral Toda lattice hierarchy J. Math. Phys. 48 023515
28. Levi D, Ragnisco O and Rodriguez M A 1993 On nonisospectral flows, Painlevé equations, and symmetries of differential and difference equations Theor. Math. Phys. 93 1409-14
29. Periwal V and Shevitz D 1990 Unitary-matrix models as exactly solvable string theories Phys. Rev. Lett. 64 1326-9
30. Fokas A S, Its A R and Kitaev A V 1991 Discrete Painlevé equations and their appearance in quantum gravity Commun. Math. Phys. 142 313-44
31. Calogero F and Degasperis A 1982 Spectral Transform and Solitons I (Amsterdam: North-Holland)
32. Bogoyavlenskii O I 1990 Overturning solitons in two-dimensional integrable equations Usp. Mat. Nauk 45 17-77
33. Gordoa P R and Pickering A 1999 Nonisospectral scattering problems: a key to intergable hierarchies J. Math. Phys. 40 5749-86
34. Pritula G M and Vekslerchik V E 2003 Negative Volterra flows J. Phys. A: Math. Gen. 36 213-26