Abstract

Multisoliton interactions are studied with an asymptotic expansion of the N-soliton solution in the limit of large frequency separation between the channels. In this limit the spectral distortion is small and the peak frequency shift of a channel is the sum of pairwise shifts as a result of interaction with other channels. These results, derived for collisions among an arbitrary number of channels, will be useful in estimating the limits on the minimum channel spacings and packet sizes for a wavelength-multiplexed optical communication system.

© 1995 Optical Society of America

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References

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  1. L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electon. Lett. 29, 910 (1993).
    [CrossRef]
  2. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [CrossRef] [PubMed]
  3. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  4. L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
    [CrossRef]
  5. A. F. Benner, J. R. Sauer, M. J. Ablowitz, J. Opt. Soc. Am. B 10, 2331 (1993).
    [CrossRef]
  6. A. F. Benner, Ph.D. dissertation (University of Colorado, Boulder, Boulder, Colo., 1992).
  7. A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993).
    [CrossRef]
  8. P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
    [CrossRef]
  9. Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
    [CrossRef] [PubMed]
  10. A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
    [CrossRef] [PubMed]

1993

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electon. Lett. 29, 910 (1993).
[CrossRef]

A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993).
[CrossRef]

A. F. Benner, J. R. Sauer, M. J. Ablowitz, J. Opt. Soc. Am. B 10, 2331 (1993).
[CrossRef]

1992

1991

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
[CrossRef] [PubMed]

P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

1983

1972

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

Ablowitz, M. J.

Andrekson, P.

P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Benner, A. F.

A. F. Benner, J. R. Sauer, M. J. Ablowitz, J. Opt. Soc. Am. B 10, 2331 (1993).
[CrossRef]

A. F. Benner, Ph.D. dissertation (University of Colorado, Boulder, Boulder, Colo., 1992).

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

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

Harvey, G. T.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electon. Lett. 29, 910 (1993).
[CrossRef]

Hasegawa, A.

A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993).
[CrossRef]

Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
[CrossRef] [PubMed]

Haus, H. A.

Kodama, Y.

Lai, Y.

Lichtman, E.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electon. Lett. 29, 910 (1993).
[CrossRef]

Logan, R. A.

P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Mecozzi, A.

Mollenauer, L. F.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electon. Lett. 29, 910 (1993).
[CrossRef]

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Moores, J. D.

Neubelt, M. J.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electon. Lett. 29, 910 (1993).
[CrossRef]

Nyu, T.

A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993).
[CrossRef]

Olsson, N. A.

P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Sauer, J. R.

Shabat, A. B.

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

Simpson, J. R.

P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Tanbun-Ek, T.

P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Wecht, K. W.

P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

Zakharov, V. E.

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

Electon. Lett.

L. F. Mollenauer, E. Lichtman, M. J. Neubelt, G. T. Harvey, Electon. Lett. 29, 910 (1993).
[CrossRef]

J. Lightwave Technol.

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993).
[CrossRef]

P. Andrekson, N. A. Olsson, J. R. Simpson, T. Tanbun-Ek, R. A. Logan, K. W. Wecht, J. Lightwave Technol. 9, 1132 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Sov. Phys. JETP

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

Other

A. F. Benner, Ph.D. dissertation (University of Colorado, Boulder, Boulder, Colo., 1992).

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Figures (1)

Fig. 1
Fig. 1

Peak frequency shifts during a three-soliton interaction when the channels are initially coincident. The solid curve is the normalized frequency shift of channel 3 ξδω3 versus normalized time 4ξT. The dashed curves represent the shifts of channel 3 that are due to its pairwise interactions with channels 1 and 2; the smaller shift corresponds to the interaction between the channels 1 and 3. For the remaining channels δω2 = 0 and δω1 = −δω3 during this interaction.

Equations (10)

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u ( X , T ) = k = 1 N q k ( X , T ) = k , j = 1 N ( A - 1 ) k j ,
u ( X , T ) = k = 1 N ( D - 1 ) k k - k , j = 1 k j N ( D - 1 M D - 1 ) k j + .
u ( X , T ) = k = 1 N q k ( 0 ) ( X , T ) + O ( ) ,
u ^ ( w , 0 ) k = 1 N q ^ K ( W , 0 ) ~ π k = 1 N sech [ π ( w - 2 ξ k ) 4 η k ] = k = 1 N q ^ k ( 0 ) ( w , 0 ) ,
u ( X , T ) = k = 1 N q k ( 0 ) [ 1 + i j = 1 k j N tanh S j ( k - j ) ] + O ( 2 ) .
u ^ ( ω , 0 ) = k = 1 N q ^ k ( 0 ) ( ω , 0 ) ( 1 + α k j = 1 j k N 1 k - j ) ,
δ ω k ω peak ( k ) - 2 ξ k = ( 4 π 2 ) 4 η 2 ξ j = 1 j k N 1 k - j .
δ f k = 0.0638 τ 2 Δ f j = 1 j k N 1 k - j .
q ^ k ( ω , T ) ~ sech ( π α k 2 ) [ 1 + j = 1 j k N sin ( α k ϕ k j ) ( k - j ) sinh ϕ k j ] ,
δ ω k = ( 4 π 2 ) 4 η 2 ξ j = 1 j k N ϕ k j ( k - j ) sinh ϕ k j

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