Analytic criterion for soliton instability in a nonlinear fiber array

E. W. Laedke; K. H. Spatschek; S. K. Turitsyn; V. K. Mezentsev

doi:10.1103/PhysRevE.52.5549

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Analytic criterion for soliton instability in a nonlinear fiber array

E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn

V. K. Mezentsev

Institut für Theoretische Physik I, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany

Institute of Automation and Electrometry, 630090 Novosibirsk, Russia

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Phys. Rev. E 52, 5549 – Published 1 November, 1995

DOI: https://doi.org/10.1103/PhysRevE.52.5549

Abstract

The stability problem for the so-called continuous-discrete solitons in a nonlinear fiber array is examined. We prove that the ground states are unstable if the first derivative of the ‘‘energy’’ integral P= ${tsum}_{n}$ F‖ $Ψ_{n}$ $‖^{2}$ dt with respect to the soliton parameter $λ^{2}$ is negative.

References (18)

A. I. Kaplan, Phys. Rev. Lett. 55, 1291 (1985).
E. W. Laedke and K. H. Spatschek, in Differential Geometry, Calculus of Variations, and Their Applications, edited by G. M. Rassias and T. M. Rassias (Marcel Dekker, Inc., New York, 1985).
E. A. Kuznetsov, A. M. Rubenchik and V. E. Zakharov, Phys. Rep. 142, 105 (1986).
R. A. Enns, S. S. Rangnekar, and A. E. Kaplan, Phys. Rev. A 35, 466 (1987).
M. J. Ablowitz and J. F. Ladik, Stud. Appl. Math. 55, 213 (1976).
A. C. Scott and L. Macneil, Phys. Lett. A 98, 87 (1983).
Yu. S. Kivshar and M. Peyrard, Phys. Rev. A 46, 3198 (1992).
O. Bang, J. J. Rasmussen and P. L. Christiansen, Nonlinearity 7, 205 (1993).
E. W. Laedke, K. H. Spatschek and S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994).
D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
C. Schmidt Hattenberger, U. Trutschel, R. Muschall and F. Lederer, Opt. Commun. 89, 473 (1992); Opt. Quantum Electron. 25, 185 (1993).
A. B. Aceves, C. De Angelis, A. M. Rubenchik and S. K. Turitsyn, Opt. Lett. 19, 329 (1994).
A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik and S. K. Turitsyn, Opt. Fiber Technol. 2, 1 (1995).
Yu. S. Kivshar, Phys. Rev. E 48, 4132 (1993).
S. N. Vlasov, V. A. Petrishchev and V. I. Talanov, Radiophys. Quantum Electron. 14, 1062 (1971).
A. V. Buryak and N. N. Akhmediev, IEEE J. Quantum Electron. 31, 682 (1995) .
F. V. Kustmartsev, Phys. Rep. 183, 1 (1989).
V. K. Mezentsev, S. L. Musher, I. V. Ryuzhenkova and S. K. Turitsyn, Pis'ma Zh. Eksp. Teor. Fiz. 22, 11 (1994) [JETP Lett. 60, 829 (1994)].

[c1] A. I. Kaplan, Phys. Rev. Lett. 55, 1291 (1985).

[c2] E. W. Laedke and K. H. Spatschek, in Differential Geometry, Calculus of Variations, and Their Applications, edited by G. M. Rassias and T. M. Rassias (Marcel Dekker, Inc., New York, 1985).

[c3] E. A. Kuznetsov, A. M. Rubenchik and V. E. Zakharov, Phys. Rep. 142, 105 (1986).

[c4] R. A. Enns, S. S. Rangnekar, and A. E. Kaplan, Phys. Rev. A 35, 466 (1987).

[c5] M. J. Ablowitz and J. F. Ladik, Stud. Appl. Math. 55, 213 (1976).

[c6] A. C. Scott and L. Macneil, Phys. Lett. A 98, 87 (1983).

[c7] Yu. S. Kivshar and M. Peyrard, Phys. Rev. A 46, 3198 (1992).

[c8] O. Bang, J. J. Rasmussen and P. L. Christiansen, Nonlinearity 7, 205 (1993).

[c9] E. W. Laedke, K. H. Spatschek and S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994).

[c10] D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).

[c11] C. Schmidt Hattenberger, U. Trutschel, R. Muschall and F. Lederer, Opt. Commun. 89, 473 (1992); Opt. Quantum Electron. 25, 185 (1993).

[c12] A. B. Aceves, C. De Angelis, A. M. Rubenchik and S. K. Turitsyn, Opt. Lett. 19, 329 (1994).

[c13] A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik and S. K. Turitsyn, Opt. Fiber Technol. 2, 1 (1995).

[c14] Yu. S. Kivshar, Phys. Rev. E 48, 4132 (1993).

[c15] S. N. Vlasov, V. A. Petrishchev and V. I. Talanov, Radiophys. Quantum Electron. 14, 1062 (1971).

[c16] A. V. Buryak and N. N. Akhmediev, IEEE J. Quantum Electron. 31, 682 (1995) .

[c17] F. V. Kustmartsev, Phys. Rep. 183, 1 (1989).

[c18] V. K. Mezentsev, S. L. Musher, I. V. Ryuzhenkova and S. K. Turitsyn, Pis'ma Zh. Eksp. Teor. Fiz. 22, 11 (1994) [JETP Lett. 60, 829 (1994)].

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Analytic criterion for soliton instability in a nonlinear fiber array

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References (18)

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