A note on an integrable discretization of the nonlinear Schrödinger equation

Inverse Problems

Volumn 13, Issue 4, 1997, Pages 1121-1136

  Suris, Yuri B ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3342906145     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/13/4/016     Document Type: Article

References (20)

1. Suris Yu B 1995 Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice Phys. Lett. A 206 153-61
2. Suris Yu B 1996 A discrete-time relativistic Toda lattice J. Phys. A: Math. Gen. 29 451-65
3. Suris Yu B 1996 Integrable discretizations of the Bogoyavlensky lattices J. Math. Phys. 37 3982-96
4. Suris Yu B 1996 A discrete time peakons lattice Phys. Lett. A 217 321-9.
5. Ablowitz M J and Ladik J F 1976 Nonlinear differential-difference equations and Fourier analysis J. Math. Phys. 17 1011-18
6. Ablowitz M J and Ladik J F 1976 A nonlinear difference scheme and inverse scattering Stud. Appl. Math. 55213-29.
7. Ablowitz M J and Ladik J F 1977 On the solution of a class of nonlinear partial difference equations Stud. Appl. Math. 57 1-12
8. Taha T R and Ablowitz M J 1984 Analytical and numerical aspects of certain nonlinear evolution equations I. Analytical J. Comput. Phys. 55 192-202 Taha T R and Ablowitz M J 1984 Analytical and numerical aspects of certain nonlinear evolution equations II. Numerical, nonlinear Schrödinger equation J. Comput. Phys. 55 203-30
9. Taha T R and Ablowitz M J 1984 Analytical and numerical aspects of certain nonlinear evolution equations I. Analytical J. Comput. Phys. 55 192-202 Taha T R and Ablowitz M J 1984 Analytical and numerical aspects of certain nonlinear evolution equations II. Numerical, nonlinear Schrödinger equation J. Comput. Phys. 55 203-30
10. Faddeev L and Takhtajan L 1987 Hamiltonian Methods in the Theory of Solitons (Berlin: Springer)
11. Hairer E, Nørsett S P and Wanner G 1987 Solving ordinary differential equations Nonstiff Problems vol 1 (Berlin: Springer)
12. Suris Yu B 1990 Hamiltonian methods of Runge-Kutta type and their variational interpretation Math. Model. 2 78-87 (in Russian)
13. Sanz-Serna J M 1991 Symplectic integrators for Hamiltonian problems: an overview Acta Numerica (Cambridge: Cambridge University Press) pp 243-86
14. Kharchev S, Mironov A and Zhedanov A 1996 Faces of relativistic Toda chain Preprint hep-th/9606144 Los Alamos National Laboratory
15. Forest E and Ruth R D 1990 Fourth order symplectic integration Physica 43D 105-17 Yoshida H 1990 Construction of higher order symplectic integrators Phys. Lett. A 150 262-8 Suzuki M 1992 General theory of higher-order decomposition of exponential operators and symplectic integrators Phys. Lett. A 165 387-95
16. Forest E and Ruth R D 1990 Fourth order symplectic integration Physica 43D 105-17 Yoshida H 1990 Construction of higher order symplectic integrators Phys. Lett. A 150 262-8 Suzuki M 1992 General theory of higher-order decomposition of exponential operators and symplectic integrators Phys. Lett. A 165 387-95
17. Forest E and Ruth R D 1990 Fourth order symplectic integration Physica 43D 105-17 Yoshida H 1990 Construction of higher order symplectic integrators Phys. Lett. A 150 262-8 Suzuki M 1992 General theory of higher-order decomposition of exponential operators and symplectic integrators Phys. Lett. A 165 387-95
18. Izergin A G and Korepin V E 1981 Lattice model connected with nonlinear Schrödinger equation Sov. Phys. Dokl. 26 653-6
19. Date E, Jimbo M and Miwa T 1983 Method for generating discrete soliton equations IV J. Phys. Soc. Japan 52 761-5
20. Quispel G R W, Nijhoff F W, Capel H W and van der Linden J 1984 Linear integral equations and nonlinear difference-difference equations Physica 125A 344-80