Lie symmetries for integrable evolution equations on the lattice

Journal of Physics A: Mathematical and General

Volumn 32, Issue 47, 1999, Pages 8303-8316

  Levi, D ^a   Rodriguez M A ^b  

^a ROMA TRE UNIVERSITY   (Italy)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039756619     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/47/309     Document Type: Article

References (25)

1. Shabat A B and Yamilov R I 1990 Alg. Anal. 2 133-208 (in Russian) (Engl. transl. 1991 Leningrad Math. J. 2 377-400)
2. Shabat A B and Yamilov R I 1990 Alg. Anal. 2 133-208 (in Russian) (Engl. transl. 1991 Leningrad Math. J. 2 377-400)
3. Olver P J 1986 Applications of Lie Groups to Differential Equations 2nd edn (New York: Springer)
4. Bluman G W and Kumei S 1989 Symmetries and Differential Equations (New York: Springer)
5. Maeda S 1987 The similarity method for difference equations IMA J. Appl. Math. 38 129-34
6. Maeda S 1980 Canonical structure and symmetries for discrete systems Math. Japonica 25 405-20
7. Levi D and Winternitz P 1991 Continuous symmetries of discrete equations Phys. Lett. A 152 335-8
8. Levi D and Winternitz P 1993 Symmetries and conditional symmetries of differential-difference equations J. Math. Phys. 34 3713-30
9. Levi D and Rodríguez M A 1992 Symmetry group of partial differential equations and of differential difference equations: the Toda lattice versus the Korteweg-de Vries equation J. Phys. A: Math. Gen. 25 L975-9
10. Negro J, Nieto L M, Floreanini R and Vinet L 1996 Symmetries of the heat equation on the lattice Lett. Math. Phys. 36 351-5
11. Levi D, Vinet L and Winternitz P 1997 Lie group formalism for difference equations J. Phys. A: Math. Gen. 30 633-49
12. Levi D, Heredero R H and Winternitz P 1999 Symmetries of the discrete Burgers equation J. Math. Phys. 32 2685-95
13. Toda M 1981 Theory of Nonlinear Lattices (Berlin: Springer)
14. Flaschka H 1974 On the Toda lattice II: inverse scattering solutions Prog. Theor. Phys. 51 703-16
15. Flaschka H 1974 The Toda lattice II: existence of integrals Phys. Rev. B 9 1924-5
16. Bruschi M, Manakov S V, Ragnisco O and Levi D 1980 The nonabelian Toda lattice - discrete analogue of the matrix Schrödinger equation J. Math. Phys. 21 2749-53
17. Bruschi M and Ragnisco O 1981 Nonlinear differential-difference matrix equations with n-dependent coefficients Lett. Nuovo Cimento 31 492-6
18. Magri F 1978 A simple model of the integrable Hamiltonian equation J. Math. Phys. 19 1156-62
19. Fuchssteiner B 1979 Application of hereditary symmetries to nonlinear evolution equations Nonlinear Anal. Theory Methods Appl. 3 849-62
20. Fuchssteiner B 1983 Mastersymmetries, high order time-dependent symmetries and conserved densities of nonlinear evolution equations Prog. Theor. Phys. 70 1508-22
21. Bruschi M, Levi D and Ragnisco O 1980 Extension of the Zakharov-Shabat generalized inverse method to solve differential-difference and difference-difference equations Nuovo Cimento A 58 56-66
22. Bruschi M, Levi D and Ragnisco O 1981 Evolution equations associated with the discrete analog of the matrix Schrödinger spectral problem solvable by the inverse spectral transform J. Math. Phys. 22 2463-71
23. Clarkson P A and Nijhoff F W (ed) 1999 Symmetries and Integrability of Difference Equations (Cambridge: Cambridge University Press)
24. Levi D, Ragnisco O and Rodríguez M A 1992 On non-isospectral flows, Painlevé equations and symmetries of differential and difference equations Teor. Mat. Fizika 93 473-80
25. Quispel G R W, Capel H W and Sahadevan R 1992 Continuous symmetries of differential-difference equations: the Kac-van Moerbeke equation and Painlevé reduction Phys. Lett. A 170 379-83