On the gauge equivalent structure of the discrete nonlinear Schrödinger equation. (English) Zbl 0949.37048
Summary: By using new Lax pairs, we prove that the continuous limits of the gauge equivalent structures of the discrete nonlinear Schrödinger equation for \(\kappa=1\) and \(-1\) are exactly the classical ones of the nonlinear Schrödinger equation for \(\kappa=1\) and \(-1\) respectively.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
References:
| [1] | M.J. Ablowitz, J.F. Ladik, J. Math. Phys. 16 (1975) 598; J. Math. Phys. 17 (1976) 1011.; M.J. Ablowitz, J.F. Ladik, J. Math. Phys. 16 (1975) 598; J. Math. Phys. 17 (1976) 1011. |
| [2] | Hennig, D.; Sun, N. G.; Gabriel, H.; Tsironis, G. P., Phys. Rev. E, 52, 255 (1995) |
| [3] | Vekslerchik, V. E.; Konotop, V. V., Inverse Problems, 8, 889 (1992) · Zbl 0766.35054 |
| [4] | Konotop, V. V.; Vekslerchik, V. E., J. Phys. A Math. Gen, 24, 767 (1991) · Zbl 0736.35109 |
| [5] | Konotop, V. V.; Vekslerchik, V. E., J. Phys. A Math. Gen, 25, 4037 (1992) · Zbl 0756.35093 |
| [6] | Roy Chowdhury, A.; Mahato, G., Lett. Math. Phys., 7, 313 (1983) · Zbl 0551.35074 |
| [7] | Holstein, T., Ann. Phys., 8, 325 (1959) |
| [8] | Takeno, S.; Hori, K.; Phys, L., Soc. Japan, 59, 3037 (1990) |
| [9] | Kenkre, V. M.; Campbell, D. K., Phys. Rev. B, 34, 4959 (1986) |
| [10] | L.D. Faddeev, L.A. Takhtajan, Hamiltonian Methods in the Theory of Solitons (Springer-Verlag 1987).; L.D. Faddeev, L.A. Takhtajan, Hamiltonian Methods in the Theory of Solitons (Springer-Verlag 1987). · Zbl 1111.37001 |
| [11] | Zakharov, V. E.; Takhtajan, L. A., Theor. Math. Phys., 38, 17 (1979) |
| [12] | Ding, Q., Phys. Lett. A, 248, 49 (1998) · Zbl 1115.35368 |
| [13] | Ding, Q., J. Phys. A: Math. Gen., 32, 5087 (1999) · Zbl 0941.35104 |
| [14] | Myrzakulov, R.; Vilayalakshmi, S.; Syzdykova, N. R.; Lakahmanan, M., J. Math. Phys., 39, 2122 (1998) · Zbl 1001.37057 |
| [15] | Ishimori, Y., J. Phys. Soc. Japan, 52, 3417 (1982) |
| [16] | Roy Chowdhury, A.; De, M., J. Phys. Soc. Japan, 58, 817 (1989) |
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