Conditions for the existence of higher symmetries of evolutionary equations on the lattice

Journal of Mathematical Physics

Volumn 38, Issue 12, 1997, Pages 6648-6674

  Levi, D ^a   Yamilov, R ^b,c  

^a ROMA TRE UNIVERSITY   (Italy)

^b UNIVERSITY OF LEEDS   (United Kingdom)

^c INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031530864     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532230     Document Type: Article

References (32)

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2. M. J. Ablowitz and J. Ladik, "Nonlinear differential-difference equations," J. Math. Phys. 16, 598-603 (1975); "Non-linear differential-difference equations and Fourier transform," ibid. 17, 1011-1018 (1976); "On the solution of a class of nonlinear partial difference equations," Stud. Appl. Math. 55, 213-229 (1976); "On the solution of a class of nonlinear partial difference equations," ibid. 57, 1 (1976).
3. M. J. Ablowitz and J. Ladik, "Nonlinear differential-difference equations," J. Math. Phys. 16, 598-603 (1975); "Non- linear differential-difference equations and Fourier transform," ibid. 17, 1011-1018 (1976); "On the solution of a class of nonlinear partial difference equations," Stud. Appl. Math. 55, 213-229 (1976); "On the solution of a class of nonlinear partial difference equations," ibid. 57, 1 (1976).
4. M. J. Ablowitz and J. Ladik, "Nonlinear differential-difference equations," J. Math. Phys. 16, 598-603 (1975); "Non- linear differential-difference equations and Fourier transform," ibid. 17, 1011-1018 (1976); "On the solution of a class of nonlinear partial difference equations," Stud. Appl. Math. 55, 213-229 (1976); "On the solution of a class of nonlinear partial difference equations," ibid. 57, 1 (1976).
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6. R. I. Yamilov, "Generalizations of the Tocla model, and conservation laws," preprint. Institute of Mathematics, Ufa, 1989 (in Russian); English version: R. I. Yamilov, Classification of Toda Type Scalar Lattices, Proceedings of the International Conference NEEDS '92 (World Scientific, Singapore, 1993).
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10. D. Levi and O. Ragnisco, "Nonlinear differential difference equations with n-dependent coefficients I," J. Phys. A 12, L157-L162 (1979); "Nonlinear differential difference equations with n-dependent coefficients II," ibid. 12, L163-L167 (1979); "The inhomogeneous Toda Lattice: Its hierarchy and Darboux-Backlund transformations," ibid. 24, 1729-39 (1991); R. Benguria and D. Levi, "Backlund transformations and nonlinear differential difference equations," Proc. Natl. Acad. Sci. USA 77, 5025-5027 (1980); D. Levi, L. Pilloni, and P. M. Santini, "Integrable three dimensional lattices," J. Phys. A 14, 1567-1575 (1981); M. Bruschi, D. Levi, and O. Ragnisco, "Evolution equations associated with the discrete analogue of the matrix Schroedinger spectral problem solvable by the inverse spectral transform," J. Math. Phys. 22, 2463-2471 (1981); "Toda lattice and generalized Wronskian technique," J. Phys. A 13, 2531-2533 (1980); "The discrete chiral field hierarchy," Lett. Nuovo Cimento 33, 284-288 (1982); "Continuous and discrete matrix Burgers hierarchies," Nuovo Cimento B 74, 33-51 (1983).
11. D. Levi and O. Ragnisco, "Nonlinear differential difference equations with n-dependent coefficients I," J. Phys. A 12, L157-L162 (1979); "Nonlinear differential difference equations with n-dependent coefficients II," ibid. 12, L163-L167 (1979); "The inhomogeneous Toda Lattice: Its hierarchy and Darboux-Backlund transformations," ibid. 24, 1729-39 (1991); R. Benguria and D. Levi, "Backlund transformations and nonlinear differential difference equations," Proc. Natl. Acad. Sci. USA 77, 5025-5027 (1980); D. Levi, L. Pilloni, and P. M. Santini, "Integrable three dimensional lattices," J. Phys. A 14, 1567-1575 (1981); M. Bruschi, D. Levi, and O. Ragnisco, "Evolution equations associated with the discrete analogue of the matrix Schroedinger spectral problem solvable by the inverse spectral transform," J. Math. Phys. 22, 2463-2471 (1981); "Toda lattice and generalized Wronskian technique," J. Phys. A 13, 2531-2533 (1980); "The discrete chiral field hierarchy," Lett. Nuovo Cimento 33, 284-288 (1982); "Continuous and discrete matrix Burgers hierarchies," Nuovo Cimento B 74, 33-51 (1983).
12. D. Levi and O. Ragnisco, "Nonlinear differential difference equations with n-dependent coefficients I," J. Phys. A 12, L157-L162 (1979); "Nonlinear differential difference equations with n-dependent coefficients II," ibid. 12, L163-L167 (1979); "The inhomogeneous Toda Lattice: Its hierarchy and Darboux-Backlund transformations," ibid. 24, 1729-39 (1991); R. Benguria and D. Levi, "Backlund transformations and nonlinear differential difference equations," Proc. Natl. Acad. Sci. USA 77, 5025-5027 (1980); D. Levi, L. Pilloni, and P. M. Santini, "Integrable three dimensional lattices," J. Phys. A 14, 1567-1575 (1981); M. Bruschi, D. Levi, and O. Ragnisco, "Evolution equations associated with the discrete analogue of the matrix Schroedinger spectral problem solvable by the inverse spectral transform," J. Math. Phys. 22, 2463-2471 (1981); "Toda lattice and generalized Wronskian technique," J. Phys. A 13, 2531-2533 (1980); "The discrete chiral field hierarchy," Lett. Nuovo Cimento 33, 284-288 (1982); "Continuous and discrete matrix Burgers hierarchies," Nuovo Cimento B 74, 33-51 (1983).
13. D. Levi and O. Ragnisco, "Nonlinear differential difference equations with n-dependent coefficients I," J. Phys. A 12, L157-L162 (1979); "Nonlinear differential difference equations with n-dependent coefficients II," ibid. 12, L163-L167 (1979); "The inhomogeneous Toda Lattice: Its hierarchy and Darboux-Backlund transformations," ibid. 24, 1729-39 (1991); R. Benguria and D. Levi, "Backlund transformations and nonlinear differential difference equations," Proc. Natl. Acad. Sci. USA 77, 5025-5027 (1980); D. Levi, L. Pilloni, and P. M. Santini, "Integrable three dimensional lattices," J. Phys. A 14, 1567-1575 (1981); M. Bruschi, D. Levi, and O. Ragnisco, "Evolution equations associated with the discrete analogue of the matrix Schroedinger spectral problem solvable by the inverse spectral transform," J. Math. Phys. 22, 2463-2471 (1981); "Toda lattice and generalized Wronskian technique," J. Phys. A 13, 2531-2533 (1980); "The discrete chiral field hierarchy," Lett. Nuovo Cimento 33, 284-288 (1982); "Continuous and discrete matrix Burgers hierarchies," Nuovo Cimento B 74, 33-51 (1983).
14. D. Levi and O. Ragnisco, "Nonlinear differential difference equations with n-dependent coefficients I," J. Phys. A 12, L157-L162 (1979); "Nonlinear differential difference equations with n-dependent coefficients II," ibid. 12, L163-L167 (1979); "The inhomogeneous Toda Lattice: Its hierarchy and Darboux-Backlund transformations," ibid. 24, 1729-39 (1991); R. Benguria and D. Levi, "Backlund transformations and nonlinear differential difference equations," Proc. Natl. Acad. Sci. USA 77, 5025-5027 (1980); D. Levi, L. Pilloni, and P. M. Santini, "Integrable three dimensional lattices," J. Phys. A 14, 1567-1575 (1981); M. Bruschi, D. Levi, and O. Ragnisco, "Evolution equations associated with the discrete analogue of the matrix Schroedinger spectral problem solvable by the inverse spectral transform," J. Math. Phys. 22, 2463-2471 (1981); "Toda lattice and generalized Wronskian technique," J. Phys. A 13, 2531-2533 (1980); "The discrete chiral field hierarchy," Lett. Nuovo Cimento 33, 284-288 (1982); "Continuous and discrete matrix Burgers hierarchies," Nuovo Cimento B 74, 33-51 (1983).
15. D. Levi and O. Ragnisco, "Nonlinear differential difference equations with n-dependent coefficients I," J. Phys. A 12, L157-L162 (1979); "Nonlinear differential difference equations with n-dependent coefficients II," ibid. 12, L163-L167 (1979); "The inhomogeneous Toda Lattice: Its hierarchy and Darboux-Backlund transformations," ibid. 24, 1729-39 (1991); R. Benguria and D. Levi, "Backlund transformations and nonlinear differential difference equations," Proc. Natl. Acad. Sci. USA 77, 5025-5027 (1980); D. Levi, L. Pilloni, and P. M. Santini, "Integrable three dimensional lattices," J. Phys. A 14, 1567-1575 (1981); M. Bruschi, D. Levi, and O. Ragnisco, "Evolution equations associated with the discrete analogue of the matrix Schroedinger spectral problem solvable by the inverse spectral transform," J. Math. Phys. 22, 2463-2471 (1981); "Toda lattice and generalized Wronskian technique," J. Phys. A 13, 2531-2533 (1980); "The discrete chiral field hierarchy," Lett. Nuovo Cimento 33, 284-288 (1982); "Continuous and discrete matrix Burgers hierarchies," Nuovo Cimento B 74, 33-51 (1983).
16. D. Levi and O. Ragnisco, "Nonlinear differential difference equations with n-dependent coefficients I," J. Phys. A 12, L157-L162 (1979); "Nonlinear differential difference equations with n-dependent coefficients II," ibid. 12, L163-L167 (1979); "The inhomogeneous Toda Lattice: Its hierarchy and Darboux-Backlund transformations," ibid. 24, 1729-39 (1991); R. Benguria and D. Levi, "Backlund transformations and nonlinear differential difference equations," Proc. Natl. Acad. Sci. USA 77, 5025-5027 (1980); D. Levi, L. Pilloni, and P. M. Santini, "Integrable three dimensional lattices," J. Phys. A 14, 1567-1575 (1981); M. Bruschi, D. Levi, and O. Ragnisco, "Evolution equations associated with the discrete analogue of the matrix Schroedinger spectral problem solvable by the inverse spectral transform," J. Math. Phys. 22, 2463-2471 (1981); "Toda lattice and generalized Wronskian technique," J. Phys. A 13, 2531-2533 (1980); "The discrete chiral field hierarchy," Lett. Nuovo Cimento 33, 284-288 (1982); "Continuous and discrete matrix Burgers hierarchies," Nuovo Cimento B 74, 33-51 (1983).
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