Gauge equivalence and l-reductions of the differential-difference KP equation

Chaos, solitons and fractals

Volumn 11, Issue 1, 2000, Pages 137-143

  Tamizhmani, K M ^a   Kanaga Vel, S ^a  

^a PONDICHERRY UNIVERSITY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENCE EQUATIONS; INTEGRATION; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS;

DIFFERENTIAL-DIFFERENCE KP EQUATIONS; GAUGE EQUIVALENCE; SATO THEORY; SOLITON EQUATIONS;

SOLITONS;

EID: 0343963094     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00277-X     Document Type: Article

References (19)

1. M. Sato, Y. Sato, Soliton equations as dynamical systems on infinite Grassmann manifold in: Nonlinear Partial Differential Equations in Applied Science, H. Fujita, P.D. Lax, G. Strang (Eds.), Kinokuniya/North-Holland, Tokyo, 1983, pp. 259-271.
2. E. Date, M. Jimbo, T. Miwa, Method for Generating Discrete Soliton Equations I-V, J. Phys. Soc. Jpn. 51 (1982) 4116-4124, 4125-4131;
3. E. Date, M. Jimbo, T. Miwa, J. Phys. Soc. Jpn. 52 (1983) 388-393, 761-765, 766-771.
4. Y. Ohta, J. Satsuma, D. Takahashi, T. Tokihiro, An elementary introduction to Sato theory, Prog. Theor. Phys. Suppl. 94 (1988) 210-241.
5. J. Matsukidaira, J. Satsuma, W. Strampp, Conserved quantities and symmetries of KP hierarchy, J. Math. Phys. 31 (1990) 1426.
6. K. Kajiwara, J. Matsukidaira, J. Satsuma, Conserved quantities of two component KP hierarchy, Phys. Lett. 146A (1990) 115.
7. B. Konopelchenko, W. Oevel, An r-matrix approach to nonstandard classes of integrable equations, Publ. RIMS. Kyoto Univ. 29 (1993) 581-666.
8. W. Oevel, C. Rogers, Gauge transformations and reciprocal links in 2+1 dimensions, Rev. Math. Phys. 5 (1993) 299-330.
9. S. Kanaga Vel, K.M. Tamizhmani, Lax pairs symmetries and conservation laws of a differential-difference equation-Sato's approach, Chaos, Solitons and Fractals 8 (1997) 917-931.
10. T. Tamizhmani, S. Kanaga vel, K.M. Tamizhmani, Wronskian and rational solutions of differential-difference KP equation, J. Phys. A: Math. Gen. 31 (1998) 7627-7633.
11. A. Ramani, B. Grammaticos, K.M. Tamizhmani, An integrability test for differential-difference systems, J. Phys. A: Math. Gen. 25 (1992) L883-L886.
12. A. Ramani, B. Grammaticos, K.M. Tamizhmani, Painlevé analysis and singularity confinement: the ultimate conjecture, J. Phys. A: Math. Gen. 26 (1993) L53-L58.
13. K.M. Tamizhmani, S. Kanagavel, B. Grammaticos, A. Ramani, Singularity confinement and symmetries of differential-difference KP equation, Chaos, Solitons & Fractals (to appear).
14. W. Oevel, Poisson brackets for integrable lattice systems, in: Algebraic Aspects of Integrable Systems: In Memory of Irne Dorfman, A.S. Fokas, I.M. Gelfand, (Eds.), Birkhäuser, Boston, 1996, pp. 261-283 .
15. A.P. Veselov, A.B. Shabat, Dressing chains and the spectral theory of the Schrödinger operator, Funct. Anal. Appn. 27 (1993) 81-96.
16. M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, 1991.
17. J. Weiss, Bäcklund Transformations and the Painlevé Property in Partially Integrable equations, R. Conte, N. Boccara (Eds.), NATO ASI Series C: Mathematical and Physical Sciences, vol. 310, Kluwer, Dordrecht, 1990, pp. 375-411.
18. R. Hirota, Reduction of soliton equations in bilinear form, Physica 18D (1986) 161-170.
19. J. Sideorenko, W. Strampp, Symmetry constraints of the KP hierarchy, Inv. Prob. 7 (1991) L37-L43.