On the integrability of a new discrete nonlinear Schrödinger equation

Journal of Physics A: Mathematical and General

Volumn 34, Issue 41, 2001, Pages

  Levi, D ^a   Yamilov, R ^b  

^a ROMA TRE UNIVERSITY   (Italy)

^b INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035914288     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/41/102     Document Type: Article

References (20)

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2. Leon J and Manna M 1999 Multiscale analysis of discrete nonlinear evolution equations J. Phys. A: Math. Gen. 32 2845-69
3. Calogero F and Eckhaus W 1987 Necessary conditions for integrability of nonlinear PDEs Inverse Problems 3 L27-32 Calogero F and Eckhaus W 1987 Nonlinear evolution equations, rescalings, model PDEs and their integrability: I Inverse Problems 3 229-63 Calogero F and Eckhaus W 1988 Nonlinear evolution equations, rescalings, model PDEs and their integrability: II Inverse Problems 4 11-33
4. Calogero F and Eckhaus W 1987 Necessary conditions for integrability of nonlinear PDEs Inverse Problems 3 L27-32 Calogero F and Eckhaus W 1987 Nonlinear evolution equations, rescalings, model PDEs and their integrability: I Inverse Problems 3 229-63 Calogero F and Eckhaus W 1988 Nonlinear evolution equations, rescalings, model PDEs and their integrability: II Inverse Problems 4 11-33
5. Calogero F and Eckhaus W 1987 Necessary conditions for integrability of nonlinear PDEs Inverse Problems 3 L27-32 Calogero F and Eckhaus W 1987 Nonlinear evolution equations, rescalings, model PDEs and their integrability: I Inverse Problems 3 229-63 Calogero F and Eckhaus W 1988 Nonlinear evolution equations, rescalings, model PDEs and their integrability: II Inverse Problems 4 11-33
6. Flashka H 1974 The Toda lattice. I. Existence of integrals Phys. Rev. B 9 1924-5 Ablowitz M J and Ladik J F 1976 Nonlinear differential-difference equations and Fourier analysis J. Math. Phys. 17 1011-8 Oevel W, Zhang H and Fuchssteiner B 1989 Mastersymmetries and multi-Hamiltonian formulations for some integrable lattice systems Progr. Theor. Phys. 81 294-308 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 Levi D 1979 The spectral transform as a tool for solving nonlinear discrete evolution equations Proc. IX Int. Seminar on Nonlinear Problems in Theoretical Physics (Lecture Notes in Physics 98) ed A F Ranada (Berlin: Springer) Levi D 1998 Equations defined on the lattice and their solutions Nonlinearity and Geometry ed D Wojcik and J Cieslinski (Warsaw: Polish Scientific Publishers PWN) pp 179-206 Hernandez Heredero R, Levi D, Rodriguez M A and Winternitz P 2000 Lie algebra contractions and symmetries of the Toda hierarchy J. Phys. A: Math. Gen. 33 5025
7. Flashka H 1974 The Toda lattice. I. Existence of integrals Phys. Rev. B 9 1924-5 Ablowitz M J and Ladik J F 1976 Nonlinear differential-difference equations and Fourier analysis J. Math. Phys. 17 1011-8 Oevel W, Zhang H and Fuchssteiner B 1989 Mastersymmetries and multi-Hamiltonian formulations for some integrable lattice systems Progr. Theor. Phys. 81 294-308 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 Levi D 1979 The spectral transform as a tool for solving nonlinear discrete evolution equations Proc. IX Int. Seminar on Nonlinear Problems in Theoretical Physics (Lecture Notes in Physics 98) ed A F Ranada (Berlin: Springer) Levi D 1998 Equations defined on the lattice and their solutions Nonlinearity and Geometry ed D Wojcik and J Cieslinski (Warsaw: Polish Scientific Publishers PWN) pp 179-206 Hernandez Heredero R, Levi D, Rodriguez M A and Winternitz P 2000 Lie algebra contractions and symmetries of the Toda hierarchy J. Phys. A: Math. Gen. 33 5025
8. Flashka H 1974 The Toda lattice. I. Existence of integrals Phys. Rev. B 9 1924-5 Ablowitz M J and Ladik J F 1976 Nonlinear differential-difference equations and Fourier analysis J. Math. Phys. 17 1011-8 Oevel W, Zhang H and Fuchssteiner B 1989 Mastersymmetries and multi-Hamiltonian formulations for some integrable lattice systems Progr. Theor. Phys. 81 294-308 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 Levi D 1979 The spectral transform as a tool for solving nonlinear discrete evolution equations Proc. IX Int. Seminar on Nonlinear Problems in Theoretical Physics (Lecture Notes in Physics 98) ed A F Ranada (Berlin: Springer) Levi D 1998 Equations defined on the lattice and their solutions Nonlinearity and Geometry ed D Wojcik and J Cieslinski (Warsaw: Polish Scientific Publishers PWN) pp 179-206 Hernandez Heredero R, Levi D, Rodriguez M A and Winternitz P 2000 Lie algebra contractions and symmetries of the Toda hierarchy J. Phys. A: Math. Gen. 33 5025
9. Flashka H 1974 The Toda lattice. I. Existence of integrals Phys. Rev. B 9 1924-5 Ablowitz M J and Ladik J F 1976 Nonlinear differential-difference equations and Fourier analysis J. Math. Phys. 17 1011-8 Oevel W, Zhang H and Fuchssteiner B 1989 Mastersymmetries and multi-Hamiltonian formulations for some integrable lattice systems Progr. Theor. Phys. 81 294-308 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 Levi D 1979 The spectral transform as a tool for solving nonlinear discrete evolution equations Proc. IX Int. Seminar on Nonlinear Problems in Theoretical Physics (Lecture Notes in Physics 98) ed A F Ranada (Berlin: Springer) Levi D 1998 Equations defined on the lattice and their solutions Nonlinearity and Geometry ed D Wojcik and J Cieslinski (Warsaw: Polish Scientific Publishers PWN) pp 179-206 Hernandez Heredero R, Levi D, Rodriguez M A and Winternitz P 2000 Lie algebra contractions and symmetries of the Toda hierarchy J. Phys. A: Math. Gen. 33 5025
10. Flashka H 1974 The Toda lattice. I. Existence of integrals Phys. Rev. B 9 1924-5 Ablowitz M J and Ladik J F 1976 Nonlinear differential-difference equations and Fourier analysis J. Math. Phys. 17 1011-8 Oevel W, Zhang H and Fuchssteiner B 1989 Mastersymmetries and multi-Hamiltonian formulations for some integrable lattice systems Progr. Theor. Phys. 81 294-308 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 Levi D 1979 The spectral transform as a tool for solving nonlinear discrete evolution equations Proc. IX Int. Seminar on Nonlinear Problems in Theoretical Physics (Lecture Notes in Physics 98) ed A F Ranada (Berlin: Springer) Levi D 1998 Equations defined on the lattice and their solutions Nonlinearity and Geometry ed D Wojcik and J Cieslinski (Warsaw: Polish Scientific Publishers PWN) pp 179-206 Hernandez Heredero R, Levi D, Rodriguez M A and Winternitz P 2000 Lie algebra contractions and symmetries of the Toda hierarchy J. Phys. A: Math. Gen. 33 5025
11. Flashka H 1974 The Toda lattice. I. Existence of integrals Phys. Rev. B 9 1924-5 Ablowitz M J and Ladik J F 1976 Nonlinear differential-difference equations and Fourier analysis J. Math. Phys. 17 1011-8 Oevel W, Zhang H and Fuchssteiner B 1989 Mastersymmetries and multi-Hamiltonian formulations for some integrable lattice systems Progr. Theor. Phys. 81 294-308 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 Levi D 1979 The spectral transform as a tool for solving nonlinear discrete evolution equations Proc. IX Int. Seminar on Nonlinear Problems in Theoretical Physics (Lecture Notes in Physics 98) ed A F Ranada (Berlin: Springer) Levi D 1998 Equations defined on the lattice and their solutions Nonlinearity and Geometry ed D Wojcik and J Cieslinski (Warsaw: Polish Scientific Publishers PWN) pp 179-206 Hernandez Heredero R, Levi D, Rodriguez M A and Winternitz P 2000 Lie algebra contractions and symmetries of the Toda hierarchy J. Phys. A: Math. Gen. 33 5025
12. Flashka H 1974 The Toda lattice. I. Existence of integrals Phys. Rev. B 9 1924-5 Ablowitz M J and Ladik J F 1976 Nonlinear differential-difference equations and Fourier analysis J. Math. Phys. 17 1011-8 Oevel W, Zhang H and Fuchssteiner B 1989 Mastersymmetries and multi-Hamiltonian formulations for some integrable lattice systems Progr. Theor. Phys. 81 294-308 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 Levi D 1979 The spectral transform as a tool for solving nonlinear discrete evolution equations Proc. IX Int. Seminar on Nonlinear Problems in Theoretical Physics (Lecture Notes in Physics 98) ed A F Ranada (Berlin: Springer) Levi D 1998 Equations defined on the lattice and their solutions Nonlinearity and Geometry ed D Wojcik and J Cieslinski (Warsaw: Polish Scientific Publishers PWN) pp 179-206 Hernandez Heredero R, Levi D, Rodriguez M A and Winternitz P 2000 Lie algebra contractions and symmetries of the Toda hierarchy J. Phys. A: Math. Gen. 33 5025
13. Adler V E, Shabat A B and Yamilov R I 2000 Symmetry approach to the integrability problem Teoret. Mat. Fiz. 125 (3) 355-424 (in Russian) (Engl. transl. 2000 Theor. Math. Phys. 125 (3) 1603-61)
14. Adler V E, Shabat A B and Yamilov R I 2000 Symmetry approach to the integrability problem Teoret. Mat. Fiz. 125 (3) 355-424 (in Russian) (Engl. transl. 2000 Theor. Math. Phys. 125 (3) 1603-61)
15. Yamilov R I 1993 Classification of Toda type scalar lattices Proc. 8th Int. Workshop on Nonlinear Evolution Equations and Dynamical Systems (NEEDS'92, Dubna, July 1992) ed V Makhankov, I Puzynin and O Pashaev) (Singapore: World Scientific) pp 423-31
16. Levi D and Yamilov R 1997 Conditions for the existence of higher symmetries of evolutionary equations on the lattice J. Math. Phys. 38 6648-74
17. Sokolov V V and Shabat A B 1984 Classification of integrable evolution equations Soviet Scientific Reviews, Section C, Mathematical Physics Reviews 4 221-80
18. Mikhailov A V, Shabat A B and Yamilov R I 1987 The symmetry approach to the classification of nonlinear equations. Complete lists of integrable systems Uspekhi Mat. Nauk 42 (4) 3-53 (in Russian) (Engl. transl. 1987 Russian Math. Surveys 42 (4) 1-63)
19. Mikhailov A V, Shabat A B and Yamilov R I 1987 The symmetry approach to the classification of nonlinear equations. Complete lists of integrable systems Uspekhi Mat. Nauk 42 (4) 3-53 (in Russian) (Engl. transl. 1987 Russian Math. Surveys 42 (4) 1-63)
20. Mikhailov A V, Shabat A B and Sokolov V V 1991 The symmetry approach to classification of integrable equations What is Integrability? ed V E Zakharov (Berlin: Springer) pp 115-84