Abstract

We analyze stability of moving dissipative solitons in the one-, two, and three-dimensional cubic-quintic complex Ginzburg-Landau equations in the presence of a linear potential (linear refractive index modulation). The expressions of stability conditions and propagation trajectory of solitons are derived by means of a generalized variational approximation. Predictions of the variational analysis are fully confirmed by direct numerical simulations. The results have potential applications to using spatial dissipative solitons in optics as individually addressable and shift registers of the all-optical data processing systems.

© 2010 OSA

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    [CrossRef] [PubMed]
  8. L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58(3), 2542–2559 (1998).
    [CrossRef]
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  11. P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104(22), 223902 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
    [CrossRef]
  15. J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  20. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
    [CrossRef] [PubMed]
  21. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75(3), 033811 (2007).
    [CrossRef]
  22. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A 77(3), 033817 (2008).
    [CrossRef]
  23. D. Mihalache and D. Mazilu, “Ginzburg-Landau spatiotemporal dissipative optical solitons,” Rom. Rep. Phys. 60, 749–761 (2008).
  24. V. Skarka and N. B. Aleksić, “Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
    [CrossRef] [PubMed]
  25. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton percolation in random optical lattices,” Opt. Express 15(19), 12409–12417 (2007).
    [CrossRef] [PubMed]
  26. Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett. 34(19), 2976–2978 (2009).
    [CrossRef] [PubMed]
  27. A. Kamagate, Ph. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (2009).
    [CrossRef] [PubMed]

2010 (1)

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104(22), 223902 (2010).
[CrossRef] [PubMed]

2009 (2)

Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett. 34(19), 2976–2978 (2009).
[CrossRef] [PubMed]

A. Kamagate, Ph. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (2009).
[CrossRef] [PubMed]

2008 (4)

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

C. Cleff, B. Gütlich, and C. Denz, “Gradient induced motion control of drifting solitary structures in a nonlinear optical single feedback experiment,” Phys. Rev. Lett. 100(23), 233902 (2008).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A 77(3), 033817 (2008).
[CrossRef]

D. Mihalache and D. Mazilu, “Ginzburg-Landau spatiotemporal dissipative optical solitons,” Rom. Rep. Phys. 60, 749–761 (2008).

2007 (4)

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg-Landau equations,” Chaos 17(3), 037117 (2007).
[CrossRef] [PubMed]

N. Akhmediev, J. M. Soto-Crespo, and P. Grelu, “Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes,” Chaos 17(3), 037112 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75(3), 033811 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton percolation in random optical lattices,” Opt. Express 15(19), 12409–12417 (2007).
[CrossRef] [PubMed]

2006 (2)

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[CrossRef] [PubMed]

V. Skarka and N. B. Aleksić, “Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
[CrossRef] [PubMed]

2005 (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[CrossRef]

2002 (1)

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002).
[CrossRef]

2000 (2)

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000).
[CrossRef] [PubMed]

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

1999 (1)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

1998 (1)

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58(3), 2542–2559 (1998).
[CrossRef]

1997 (1)

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

1996 (2)

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1190–1201 (1996).
[CrossRef] [PubMed]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: Robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76(10), 1623–1626 (1996).
[CrossRef] [PubMed]

1995 (1)

M. L. van Hecke, E. de Wit, and W. van Saarloos, “Coherent and incoherent drifting pulse dynamics in a complex Ginzburg-Landau equation,” Phys. Rev. Lett. 75(21), 3830–3833 (1995).
[CrossRef] [PubMed]

Ackemann, T.

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

Afanasjev, V. V.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1190–1201 (1996).
[CrossRef] [PubMed]

Akhmediev, N.

A. Kamagate, Ph. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (2009).
[CrossRef] [PubMed]

N. Akhmediev, J. M. Soto-Crespo, and P. Grelu, “Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes,” Chaos 17(3), 037112 (2007).
[CrossRef] [PubMed]

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000).
[CrossRef] [PubMed]

Akhmediev, N. N.

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1190–1201 (1996).
[CrossRef] [PubMed]

Aleksic, N. B.

V. Skarka and N. B. Aleksić, “Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
[CrossRef] [PubMed]

Ankiewicz, A.

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000).
[CrossRef] [PubMed]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

Aranson, I. S.

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002).
[CrossRef]

Barland, S.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104(22), 223902 (2010).
[CrossRef] [PubMed]

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

Brambilla, M.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58(3), 2542–2559 (1998).
[CrossRef]

Caboche, E.

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

Christodoulides, D. N.

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

Cleff, C.

C. Cleff, B. Gütlich, and C. Denz, “Gradient induced motion control of drifting solitary structures in a nonlinear optical single feedback experiment,” Phys. Rev. Lett. 100(23), 233902 (2008).
[CrossRef] [PubMed]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[CrossRef] [PubMed]

de Wit, E.

M. L. van Hecke, E. de Wit, and W. van Saarloos, “Coherent and incoherent drifting pulse dynamics in a complex Ginzburg-Landau equation,” Phys. Rev. Lett. 75(21), 3830–3833 (1995).
[CrossRef] [PubMed]

Denz, C.

C. Cleff, B. Gütlich, and C. Denz, “Gradient induced motion control of drifting solitary structures in a nonlinear optical single feedback experiment,” Phys. Rev. Lett. 100(23), 233902 (2008).
[CrossRef] [PubMed]

Firth, W. J.

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: Robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76(10), 1623–1626 (1996).
[CrossRef] [PubMed]

Genevet, P.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104(22), 223902 (2010).
[CrossRef] [PubMed]

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

Giudici, M.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104(22), 223902 (2010).
[CrossRef] [PubMed]

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

Grelu, P.

N. Akhmediev, J. M. Soto-Crespo, and P. Grelu, “Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes,” Chaos 17(3), 037112 (2007).
[CrossRef] [PubMed]

Grelu, Ph.

A. Kamagate, Ph. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (2009).
[CrossRef] [PubMed]

Gütlich, B.

C. Cleff, B. Gütlich, and C. Denz, “Gradient induced motion control of drifting solitary structures in a nonlinear optical single feedback experiment,” Phys. Rev. Lett. 100(23), 233902 (2008).
[CrossRef] [PubMed]

He, Y. J.

Huang, H. C.

Jäger, R.

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

Kamagate, A.

A. Kamagate, Ph. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (2009).
[CrossRef] [PubMed]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton percolation in random optical lattices,” Opt. Express 15(19), 12409–12417 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[CrossRef] [PubMed]

Kramer, L.

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002).
[CrossRef]

Leblond, H.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A 77(3), 033817 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75(3), 033811 (2007).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A 77(3), 033817 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75(3), 033811 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[CrossRef] [PubMed]

Liu, B.

Lugiato, L. A.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58(3), 2542–2559 (1998).
[CrossRef]

Malomed, B. A.

Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett. 34(19), 2976–2978 (2009).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A 77(3), 033817 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75(3), 033811 (2007).
[CrossRef]

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg-Landau equations,” Chaos 17(3), 037117 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[CrossRef] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A 77(3), 033817 (2008).
[CrossRef]

D. Mihalache and D. Mazilu, “Ginzburg-Landau spatiotemporal dissipative optical solitons,” Rom. Rep. Phys. 60, 749–761 (2008).

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75(3), 033811 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[CrossRef] [PubMed]

Mihalache, D.

Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett. 34(19), 2976–2978 (2009).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A 77(3), 033817 (2008).
[CrossRef]

D. Mihalache and D. Mazilu, “Ginzburg-Landau spatiotemporal dissipative optical solitons,” Rom. Rep. Phys. 60, 749–761 (2008).

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75(3), 033811 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[CrossRef] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[CrossRef]

Oppo, G.-L.

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

Pedaci, F.

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

Prati, F.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58(3), 2542–2559 (1998).
[CrossRef]

Scroggie, A. J.

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: Robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76(10), 1623–1626 (1996).
[CrossRef] [PubMed]

Segev, M.

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Skarka, V.

V. Skarka and N. B. Aleksić, “Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

A. Kamagate, Ph. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (2009).
[CrossRef] [PubMed]

N. Akhmediev, J. M. Soto-Crespo, and P. Grelu, “Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes,” Chaos 17(3), 037112 (2007).
[CrossRef] [PubMed]

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000).
[CrossRef] [PubMed]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1190–1201 (1996).
[CrossRef] [PubMed]

Spinelli, L.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58(3), 2542–2559 (1998).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Tchofo-Dinda, P.

A. Kamagate, Ph. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (2009).
[CrossRef] [PubMed]

Tissoni, G.

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58(3), 2542–2559 (1998).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton percolation in random optical lattices,” Opt. Express 15(19), 12409–12417 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[CrossRef] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[CrossRef]

Tredicce, J. R.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104(22), 223902 (2010).
[CrossRef] [PubMed]

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

van Hecke, M. L.

M. L. van Hecke, E. de Wit, and W. van Saarloos, “Coherent and incoherent drifting pulse dynamics in a complex Ginzburg-Landau equation,” Phys. Rev. Lett. 75(21), 3830–3833 (1995).
[CrossRef] [PubMed]

van Saarloos, W.

M. L. van Hecke, E. de Wit, and W. van Saarloos, “Coherent and incoherent drifting pulse dynamics in a complex Ginzburg-Landau equation,” Phys. Rev. Lett. 75(21), 3830–3833 (1995).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wang, H. Z.

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[CrossRef]

Yang, H.

Appl. Phys. Lett. (1)

F. Pedaci, S. Barland, E. Caboche, P. Genevet, M. Giudici, J. R. Tredicce, T. Ackemann, A. J. Scroggie, W. J. Firth, G.-L. Oppo, G. Tissoni, and R. Jäger, “All-optical delay line using semiconductor cavity solitons,” Appl. Phys. Lett. 92(1), 011101–011103 (2008).
[CrossRef]

Chaos (2)

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg-Landau equations,” Chaos 17(3), 037117 (2007).
[CrossRef] [PubMed]

N. Akhmediev, J. M. Soto-Crespo, and P. Grelu, “Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes,” Chaos 17(3), 037112 (2007).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

J. Opt. B Quantum Semiclassical Opt. (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (3)

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75(3), 033811 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A 77(3), 033817 (2008).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58(3), 2542–2559 (1998).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Kamagate, Ph. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (2009).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(1), 1190–1201 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg-Landau equation,” Phys. Rev. Lett. 79(21), 4047–4051 (1997).
[CrossRef]

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Pulsating, creeping, and erupting solitons in dissipative systems,” Phys. Rev. Lett. 85(14), 2937–2940 (2000).
[CrossRef] [PubMed]

C. Cleff, B. Gütlich, and C. Denz, “Gradient induced motion control of drifting solitary structures in a nonlinear optical single feedback experiment,” Phys. Rev. Lett. 100(23), 233902 (2008).
[CrossRef] [PubMed]

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104(22), 223902 (2010).
[CrossRef] [PubMed]

M. L. van Hecke, E. de Wit, and W. van Saarloos, “Coherent and incoherent drifting pulse dynamics in a complex Ginzburg-Landau equation,” Phys. Rev. Lett. 75(21), 3830–3833 (1995).
[CrossRef] [PubMed]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: Robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76(10), 1623–1626 (1996).
[CrossRef] [PubMed]

V. Skarka and N. B. Aleksić, “Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002).
[CrossRef]

Rom. Rep. Phys. (1)

D. Mihalache and D. Mazilu, “Ginzburg-Landau spatiotemporal dissipative optical solitons,” Rom. Rep. Phys. 60, 749–761 (2008).

Science (1)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Other (4)

Y. S. Kivshar, and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

W. J. Firth, in Self-Organization in Optical Systems and Applications in Information Technology, edited by M. A. Vorontsov and W. B. Miller (Springer-Verlag, Berlin, 1995), p. 69.

N. N. Akhmediev, and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman and Hall, London, 1997).

B. A. Malomed, “Complex Ginzburg-Landau equation,” in: Encyclopedia of Nonlinear Science, A. Scott, ed., (Routledge, New York, 2005) pp. 157–160.

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Figures (4)

Fig. 2
Fig. 2

Numerical simulation for moving 1D dissipative soliton. (a) Stable propagation of soliton with α = 0.1 and (b) soliton decay with α = 0.3.

Fig. 3
Fig. 3

Numerical simulation for moving 2D dissipative soliton in (a) Stable propagation of soliton with α = 0.2 and (b) soliton decay with α = 0.45.

Fig. 4
Fig. 4

Numerical simulation for moving 3D dissipative soliton in (a) Stable propagation of soliton with α = 0.04 and (b) soliton decay with α = 0.1. In (a) and (b), the isosurfaces | u | = 0.8.

Fig. 1
Fig. 1

Profiles of solitons for 1D, 2D, and 3D cases, respectively, in (a), (b), and (c).

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

i u z + ( 1 / 2 ) Δ u + | u | 2 u + ν | u | 4 u = i R [ u ] α x u ,
u = A ( z ) exp { [ x q ( z ) ] 2 + y 2 + t 2 2 w 2 ( z ) + i c ( z ) [ ( x q ( z ) ) 2 + y 2 + t 2 ] + i L ( z ) [ x q ( z ) ] + i ψ ( z ) } ,
d A / d z = [ δ + 2 ( 2 + D / 2 ) ( 4 + D ) ε A 2 + 3 ( 1 + D / 2 ) ( 3 + D ) μ A 4 D β w 2 D c β L 2 ] A ,
d w / d z = [ 2 ( 1 + D / 2 ) ε A 2 2 3 ( 1 + D / 2 ) μ A 4 + β w 2 4 β c 2 w 2 + 2 c ] w ,
d c / d z = ( 2 w 4 ) 1 2 ( 1 + D / 2 ) A 2 w 2 2 3 ( 1 + D / 2 ) ν A 4 w 2 4 β c w 2 2 c 2 ,
d L / d z = α 2 β L w 2 ( 1 + 4 c 2 w 4 ) ,
d ψ / d z = 2 D β c D ( 2 w 2 ) 1 2 ( 2 + D / 2 ) ( 4 + D ) A 2 + 3 ( 1 + D / 2 ) ( 3 + D ) ν A 4 + α q + L 2 / 2 4 β c L 2 w 2 ,
d q / d z = L 4 β c L w 2 .
d ( Δ a ) / d z = b 1 Δ a + b 2 Δ w + b 3 Δ c + b 4 Δ L ,
d ( Δ w ) / d z = b 5 Δ a + b 6 Δ r + b 7 Δ c ,
d ( Δ c ) / d z = b 8 Δ a + b 9 Δ r + b 10 Δ c ,
d ( Δ L ) / d z = b 11 Δ w + b 12 Δ c + b 13 Δ L ,
| b 1 λ b 2 b 3 b 4 b 5 b 6 λ b 7 0 b 8 b 9 b 10 λ 0 0 b 11 b 12 b 13 λ | = 0.
a 1 > 0 , | a 1 1 a 3 a 2 |     > 0 , | a 1 1 0 a 3 a 2 a 1 0 a 4 a 3 |     > 0 , | a 1 1 0 0 a 3 a 2 a 1 1 0 a 4 a 3 a 2 0 0 0 a 4 |     > 0 ,
a 4 = b 4 [ b 7 b 8 b 11 + b 6 b 8 b 12 + b 5 ( b 10 b 11 b 9 b 12 ) ] + b 13 [ b 3 ( b 5 b 9 b 6 b 8 ) + b 2 ( b 7 b 8 b 5 b 10 ) + b 1 ( b 6 b 10 b 7 b 9 ) ] .
q ( z ) = α w 0 2 ( 1 4 β c 0 w 0 2 ) / [ 2 β ( 1 + 4 c 0 2 w 0 4 ) ] z .

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