On integrability and chaos in discrete systems

Chaos, solitons and fractals

Volumn 11, Issue 1, 2000, Pages 159-169

  Ablowitz, Mark J ^a   Ohta, Yasuhiro ^b   Trubatch, A David ^a  

^a UNIVERSITY OF COLORADO   (United States)

^b HIROSHIMA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; INTEGRATION; NONLINEAR EQUATIONS; VECTORS;

DISCRETE SYSTEMS; SCHRODINGER EQUATIONS;

WAVE EQUATIONS;

EID: 0033940295     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00280-X     Document Type: Article

References (23)

1. M.J. Ablowitz, S. Chakravarty, B.M. Herbst, Integrability, computation and applications, Acta Applicandae Mathematicae 39 (1995) 5-37.
2. M.J. Ablowitz, P.A. Clarkson, Solitons nonlinear evolution equations and Inverse Scattering. Number 149 in London Mathematical Society Lecture Note Series, No. 149, Cambridge Univ. Press, Cambridge, 1991.
3. M.J. Ablowitz, B.M. Herbst, C.M. Schober, Computational chaos in the nonlinear Schrödinger equation without homoclinic crossings, Physica A 228 (1996) 212-235.
4. M.J. Ablowitz, J.F. Ladik, A nonlinear difference scheme and inverse scattering, Studies in Applied Mathematics 55 (1976) 213-229.
5. M.J. Ablowitz, Y. Ohta, A.D. Trubatch, On discretizations of the vector nonlinear Schrödinger equation, Phys. Lett. A 253 (1999) 287-304.
6. M.J. Ablowitz, C.M. Schober, Effective chaos in the nonlinear Schrödinger equation, Contemporary Mathematics 172 (1994) 253-268.
7. M.J. Ablowitz, C.M. Schober, B.M. Herbst, Numerical chaos, roundoff errors and homoclinic manifolds, Physical Review Letters 71 (17) (1993) 2683-2686.
8. M.J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transfom, SIAM Studies in Applied Mathematics, No. 4, SIAM, Philadelphia, PA, 1981.
9. D. Cai, A.R. Bishop, N. Grønbech-Jensen, M. Salerno, Electric field-induced nonlinear bloch oscillations and dynamical localization, Physical Review Letters 74 (1995) 1186.
10. J.C. Eilbeck, P.S. Lombdahl, A.C. Scott, The discrete self-trapping equation, Physica D 16D (1985) 318-338.
11. S.G. Evangelides, L.F. Mollenauer, J.P. Gordon, N.S. Bergano, Polarization multiplexing with solitons, Journal of Lightwave Technology 10 (1) (1992) 28-35.
12. B.M. Herbst, M.J. Ablowitz, Numerical chaos, symplectic integrators and exponentially small splitting distances, Journal of Computational Physics 105 (1993) 122-132.
13. V.M. Kenkre, D.K. Campbell, Self-trapping on a dimer: time-dependent solutions of a discrete nonlinear Schrödinger equation, Physical Review B 34 (1986) 4959-4961.
14. V.M. Kenkre, G.P. Tsironis, Nonlinear effects in quasilinear neutron scattering: exact line calculation for a dimer, Physical Review B 35 (1987) 1473-1484.
15. T.I. Lakoba, D.J. Kaup, Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers, Physical Review E 56 (5) (1997) 6147-6165.
16. S.V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Soviet Physics JETP 38 (2) (1974) 248-253.
17. D.W. McLaughlin, E.A. Overman II, in: Whiskered Tori for Integrable PDE's: Chaotic Behavior in Near Integrable PDE's, Surveys in Applied Mathematics, vol. 1, Plenum Press, New York, 1995.
18. C.R. Menyuk, Nonlinear pulse propagation in birefringent optical fibers, IEEE Journal of Quantum Electronics QE 23 (2) (1987) 174-176.
19. C.R. Menyuk, Pulse propagation in an elliptically birefringent Kerr medium, IEEE Journal of Quantum Electronics 25 (12) (1989) 2674-2682.
20. Y. Ohta, Pfaffian solutions for coupled discrete nonlinear Schrödinger equation, Chaos, Solitons and Fractals, in: Proceedings of Brussels Meeting II: Integrability and Chaos in Discrete Systems, Brussels, 2-6 July 1997.
21. V.S. Shchesnovich, E.V. Doktorov, Perturbation theory for solitons of the Manakov system, Physical Review E 55 (6) (1997) 7626-7635.
22. Y.B. Suris, A discrete-time Gamier system, Physics Letters A 189 (4) (1994) 281-289.
23. A.D. Trabatch, Ph.D. thesis, University of Colorado, 1999.