Abstract

We study analytically and numerically the interaction of adjacent solitons under the influence of a phase modulator. Above a critical value, a bifurcation takes place and the interaction-free lengths are considerably increased.

© 1994 Optical Society of America

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References

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  1. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [CrossRef] [PubMed]
  2. K. J. Blow, N. J. Doran, Electron. Lett. 19, 429 (1983).
    [CrossRef]
  3. P. L. Chu, C. Desem, Electron. Lett. 19, 956 (1983).
    [CrossRef]
  4. M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992).
    [CrossRef]
  5. S. Wabnitz, Opt. Lett. 18, 601 (1993).
    [CrossRef] [PubMed]
  6. P.-L. François, T. Georges, Opt. Lett. 18, 583 (1993).
    [CrossRef] [PubMed]
  7. N. J. Smith, K. J. Blow, W. J. Firth, K. Smith, Opt. Commun. 102, 324 (1993).
    [CrossRef]
  8. J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
    [CrossRef]
  9. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  10. V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981).
    [CrossRef]
  11. S. R. Friberg, K. W. DeLong, Opt. Lett. 17, 979 (1992).
    [CrossRef] [PubMed]

1993 (3)

1992 (2)

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992).
[CrossRef]

S. R. Friberg, K. W. DeLong, Opt. Lett. 17, 979 (1992).
[CrossRef] [PubMed]

1983 (3)

J. P. Gordon, Opt. Lett. 8, 596 (1983).
[CrossRef] [PubMed]

K. J. Blow, N. J. Doran, Electron. Lett. 19, 429 (1983).
[CrossRef]

P. L. Chu, C. Desem, Electron. Lett. 19, 956 (1983).
[CrossRef]

1981 (1)

V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981).
[CrossRef]

1974 (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

1972 (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Blow, K. J.

N. J. Smith, K. J. Blow, W. J. Firth, K. Smith, Opt. Commun. 102, 324 (1993).
[CrossRef]

K. J. Blow, N. J. Doran, Electron. Lett. 19, 429 (1983).
[CrossRef]

Chu, P. L.

P. L. Chu, C. Desem, Electron. Lett. 19, 956 (1983).
[CrossRef]

DeLong, K. W.

Desem, C.

P. L. Chu, C. Desem, Electron. Lett. 19, 956 (1983).
[CrossRef]

Doran, N. J.

K. J. Blow, N. J. Doran, Electron. Lett. 19, 429 (1983).
[CrossRef]

Firth, W. J.

N. J. Smith, K. J. Blow, W. J. Firth, K. Smith, Opt. Commun. 102, 324 (1993).
[CrossRef]

François, P.-L.

Friberg, S. R.

Georges, T.

Gordon, J. P.

Karpman, V. I.

V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981).
[CrossRef]

Kubota, H.

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992).
[CrossRef]

Nakazawa, M.

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992).
[CrossRef]

Satsuma, J.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Smith, K.

N. J. Smith, K. J. Blow, W. J. Firth, K. Smith, Opt. Commun. 102, 324 (1993).
[CrossRef]

Smith, N. J.

N. J. Smith, K. J. Blow, W. J. Firth, K. Smith, Opt. Commun. 102, 324 (1993).
[CrossRef]

Solov’ev, V. V.

V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981).
[CrossRef]

Wabnitz, S.

Yajima, N.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Electron. Lett. (3)

K. J. Blow, N. J. Doran, Electron. Lett. 19, 429 (1983).
[CrossRef]

P. L. Chu, C. Desem, Electron. Lett. 19, 956 (1983).
[CrossRef]

M. Nakazawa, H. Kubota, Electron. Lett. 28, 958 (1992).
[CrossRef]

Opt. Commun. (1)

N. J. Smith, K. J. Blow, W. J. Firth, K. Smith, Opt. Commun. 102, 324 (1993).
[CrossRef]

Opt. Lett. (4)

Physica D (1)

V. I. Karpman, V. V. Solov’ev, Physica D 3, 487 (1981).
[CrossRef]

Prog. Theor. Phys. Suppl. (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

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Figures (3)

Fig. 1
Fig. 1

Phase space for the solitons’ frequency and position with (a) two equilibrium points and (b) no equilibrium points.

Fig. 2
Fig. 2

Collision lengths for a pair of as a function of the modulator peak phase shift.

Fig. 3
Fig. 3

Bifurcation curve of soliton–soliton interactions as a function of the pulse width.

Equations (8)

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u = A sech [ ( t T 0 ) / τ ] + A sech [ ( t + T 0 ) / τ ] ,
d ω i d z = ( 1 ) i 4 β ¨ τ 3 exp ( r / τ ) 2 α m ( T i T i 0 ) ,
d T i d z = β ¨ ω i .
d ω d z = 4 β ¨ τ 3 exp [ 2 ( T 0 + Δ T ) / τ ] 2 α m Δ T ,
d Δ T d z = β ¨ ω .
0 = 4 β ¨ τ 3 2 τ exp ( 2 T 0 / τ ) exp ( 2 Δ T / τ ) 2 α m .
Δ T = τ 2 ,
α m = 4 β ¨ τ 4 exp ( 1 2 T 0 τ ) .

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