Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations. (English) Zbl 1125.35406
Summary: We put forward the first physical model based on coupled Ginzburg-Landau equations that supports exact stable pulse solutions. The model describes a doped twin-core optical fiber with dispersive losses, dispersion, and cubic nonlinearity in one component, and pure losses in the other. The exact stable pulses are found for the cases of the anomalous, normal, and zero dispersion. Necessary conditions for stability of the pulses are obtained analytically, and a full stability analysis is performed numerically. We find nontrivial stability borders on the model’s phase planes that do not follow from elementary theorems of the bifurcation theory.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
References:
| [1] | Pereira, N. R.; Stenflo, L., Phys. Fluids, 20, 1733 (1977) · Zbl 0364.35012 |
| [2] | Soto-Crespo, J. M.; Akhmediev, N. N.; Afanasjev, V. V.; Wabnitz, S., Phys. Rev. E, 55, 4783 (1997) |
| [3] | Riecke, H., Phys. Rev. Lett., 68, 301 (1992) |
| [4] | Glazier, J. A.; Kolodner, P.; Williams, H., J. Stat. Phys., 64, 945 (1991) |
| [5] | Barashenkov, I. V.; Smirnov, Yu. S., Phys. Rev. E, 54, 5707 (1996) |
| [6] | Winful, H. G.; Walton, D. T., Opt. Lett., 17, 1688 (1992) |
| [7] | Walton, D. T.; Winful, H. G., Opt. Lett., 18, 720 (1993) |
| [8] | Malomed, B. A.; Winful, H. G., Phys. Rev. E, 53, 5365 (1996) |
| [9] | Atai, J.; Malomed, B. A., Phys. Rev. E, 54, 4371 (1996) |
| [10] | Chu, P. L.; Peng, G. D.; Malomed, B. A.; Hatami-Hansa, H.; Skinner, I. M., Opt. Lett., 20, 1092 (1995) |
| [11] | Chu, P. L.; Malomed, B. A.; Peng, G. D., Opt. Lett., 21, 330 (1996) |
| [12] | Maier, A. M., Sov. J. Quant. Electron., 12, 1490 (1982) |
| [13] | Romangoli, M.; Trillo, S.; Wabnitz, S., Opt. Quantum Electron., 24, S1237 (1992) |
| [14] | Malomed, B. A.; Skinner, I. M.; Chu, P. L.; Peng, G. D., Phys. Rev. E, 53, 4084 (1996) |
| [15] | Cross, M. C.; Hohenberg, P. C., Rev. Mod. Phys., 65, 851 (1993) · Zbl 1371.37001 |
| [16] | Hasegawa, A.; Kodama, Y., (Solitons in Optical Communications (1995), Oxford Univ. Press: Oxford Univ. Press Oxford) · Zbl 0840.35092 |
| [17] | Iooss, G.; Joseph, D. D., (Elementary Stability, Bifurcation Theory (1980), Springer: Springer New York) · Zbl 0443.34001 |
| [18] | Gölles, M.; Malomed, B. A.; Uzunov, I.; Lederer, F., Physica Scripta, 55, 73 (1997) |
| [19] | J. Atai, B.A. Malomed, Bound states of solitary pulses in linearly coupled Ginzburg-Landau equations, Phys. Lett. A, in press.; J. Atai, B.A. Malomed, Bound states of solitary pulses in linearly coupled Ginzburg-Landau equations, Phys. Lett. A, in press. · Zbl 0947.35148 |
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