Singularity structure and algebraic properties of the differential-difference Kadomtsev-Petviashvili equation

Chaos, solitons and fractals

Volumn 11, Issue 9, 2000, Pages 1423-1431

  Tamizhmani, K M ^a   Kanagavel, S ^a   Grammaticos, B ^b   Ramani, A ^c  

^a PONDICHERRY UNIVERSITY   (India)

^b UNIVERSITÉ PARIS DESCARTES   (France)

^c CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; LINEAR ALGEBRA; NONLINEAR EQUATIONS;

KADOMTSEV-PETVIASHVILI EQUATION; SATO'S THEORY;

SOLITONS;

EID: 0034217019     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(99)00059-4     Document Type: Article

References (23)

1. Ablowitz M.J., Clarkson P.A. Solitons nonlinear evolution equations and inverse scattering. 1991;Cambridge University Press, Cambridge.
2. Ramani A., Grammaticos B., Bountis T. The Painlevé property and singularity analysis of integrable and nonintegrable systems. Phys Rep. 180:1984;159.
3. Ablowitz M.J., Ramani A., Segur H. Nonlinear evolution equations and ordinary differential equations of Painlevé type. Lett Nuovo Cim. 23:1978;333.
4. Grammaticos B., Ramani A., Papgageorgiou V.G. Do integrable mappings have the Painlevé property? Phys Rev Lett. 67:1991;1825.
5. Ramani A., Grammaticos B., Tamizhmani K.M. An integrability test for differential-difference systems. J Phys A: Math Gen. 25:1992;L883.
6. Ramani A., Grammaticos B., Tamizhmani K.M. Painlevé analysis and singularity confinement: the ultimate conjecture. J Phys A: Math Gen. 26:1993;L53.
7. Date E, Jimbo M, Miwa T Method for generating discrete soliton equations I-V. J Phys Soc Japan. 52:1982;4116, 4125.
8. Date E, Jimbo M, Miwa T Method for generating discrete soliton equations I-V. J Phys Soc Japan. 52:1983;388,761,766.
9. Date E, Jimbo M, Kashiwara M, Miwa T. Transformation groups for soliton equations. In: Proceedings of the RIMS Symposium on Nonlinear Integrable Systems, Classical and Quantum Theory (Kyoto 1981), vol. 39. Singapore: World Scientific, 1983.
10. Kanagavel S., Tamizhmani K.M. Lax pairs symmetries and conservation laws of a differential-difference equation-Sato's approach. Chaos Solitons & Fractals. 8:1997;917.
11. Olver P.J. Applications of Lie groups to differential equations. 1986;Springer, New York.
12. Levi D., Winternitz P. Symmetries and conditional symmetries of differential-difference equations. J Math Phys. 34:1993;3713.
13. Levi D., Winternitz P. Symmetries of discrete dynamical systems. J Math Phys. 37:1996;5551.
14. Quispel G.R.W., Capel H.W., Sahadevan R. Continuous symmetries of differential-difference equations: the Kac-van Moerbeke equation and Painlevé reduction. Phys Lett. 170A:1992;379.
15. Sato M. Soliton equations as dynamical systems on an infinite dimensional grassmann manifold. RIMS Kokyuroku. 439:1981;30.
16. Ohta Y., Satsuma J., Takahashi D., Tokihiro T. An elementary introduction to Sato theory. Prog Theor Phys Suppl. 94:1988;210.
17. Tamizhmani KM, Kanagavel S. Gauge equivalence and l-reduction of differential-difference KP equation. Chaos, Solitons & Fractals 2000;11:137.
18. Grammaticos B., Ramani A., Moreira I.C. Delay-differential equations and the Painlevé transcendents. Physica. 196A:1993;574.
19. Grammaticos B, Ramani A. Integrability and how to detect it. In: Kosmann-Schwarzbach Y, Grammaticos B, Tamizhmani KM, editors. Integrability of nonlinear systems, Lecture Notes in Physics, Proceedings of Cimpa International Winter School on Nonlinear Systems, Pondicherry, LNP495 Berlin: Springer, 1996.
20. Veselov A.P., Shabat A.B. Dressing chains and the spectral theory of the Schrödinger operator. Funct Anal Appl. 27:1993;81.
21. Oevel W., Zhang H., Fuchssteiner B. Symmetries, conserved quantities and hierarchies for some lattice systems with soliton structure. J Math Phys. 32:1991;1908.
22. Matsukidaira J., Satsuma J., Strampp W. Conserved quantities and symmetries of KP hierarchy. J Math Phys. 31:1990;1426.
23. Oevel W. Poisson brackets for integrable lattice systems. In: Fokas AS, Gelfand IM, editors. Algebraic aspects of integrable systems: in memory of Irne Dorfman. Boston: Birkhauser, 1996:261.