Abstract

We address the stability of multipole-mode solitons in nonlocal Kerr-type nonlinear media. Such solitons comprise several out-of-phase peaks packed together by the forces acting between them. We discover that dipole-, triple-, and quadrupole-mode solitons can be made stable, whereas all higher-order soliton bound states are unstable.

© 2005 Optical Society of America

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  2. M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
    [CrossRef]
  3. E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
    [CrossRef]
  4. A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
    [CrossRef] [PubMed]
  5. D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
    [CrossRef]
  6. N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, Phys. Rev. E 68, 036614 (2003).
    [CrossRef]
  7. A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
    [CrossRef]
  8. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
    [CrossRef]
  9. M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 30, 415 (2005).
    [CrossRef] [PubMed]
  10. F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, J. Opt. A Pure Appl. Opt. 2, 332 (2000).
    [CrossRef]
  11. A. G. Litvak, V. A. Mironov, G. M. Fraiman, and A. D. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).
  12. W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2001).
    [CrossRef]
  13. W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
    [CrossRef]
  14. W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
    [CrossRef]
  15. N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
    [CrossRef] [PubMed]
  16. I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980)I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , [JETP Lett. 31, 304 (1980)].
  17. V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , Dokl. Akad. Nauk SSSR 260, 325 (1981)V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , [Sov. Phys. Dokl. 26, 861 (1981)].
  18. X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
    [CrossRef]
  19. A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, arXiv.org, e-print archive, physics/0504003, April 20, 2005.
  20. G. Agez, P. Glorieux, C. Szwaj, and E. Louvergneaux, Opt. Commun. 245, 243 (2005).
    [CrossRef]
  21. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 12, 2831 (2004).
    [CrossRef] [PubMed]
  22. Z. Y. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
    [CrossRef]

2005 (3)

M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 30, 415 (2005).
[CrossRef] [PubMed]

G. Agez, P. Glorieux, C. Szwaj, and E. Louvergneaux, Opt. Commun. 245, 243 (2005).
[CrossRef]

Z. Y. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef]

2004 (4)

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 12, 2831 (2004).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

2003 (1)

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, Phys. Rev. E 68, 036614 (2003).
[CrossRef]

2002 (1)

2001 (2)

W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2001).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
[CrossRef]

2000 (1)

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, J. Opt. A Pure Appl. Opt. 2, 332 (2000).
[CrossRef]

1999 (1)

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

1998 (1)

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

1997 (1)

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

1996 (1)

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

1995 (1)

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

1981 (1)

V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , Dokl. Akad. Nauk SSSR 260, 325 (1981)V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , [Sov. Phys. Dokl. 26, 861 (1981)].

1980 (1)

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980)I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , [JETP Lett. 31, 304 (1980)].

1975 (1)

A. G. Litvak, V. A. Mironov, G. M. Fraiman, and A. D. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).

Abbate, G.

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, J. Opt. A Pure Appl. Opt. 2, 332 (2000).
[CrossRef]

Adamski, A.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Agez, G.

G. Agez, P. Glorieux, C. Szwaj, and E. Louvergneaux, Opt. Commun. 245, 243 (2005).
[CrossRef]

Agrawal, G. P.

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

Anderson, D. Z.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Assanto, G.

Bang, O.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, Phys. Rev. E 68, 036614 (2003).
[CrossRef]

W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2001).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Boardman, A. D.

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

Brzdakiewicz, K. A.

Cambournac, C.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Christiansen, P. L.

Christodoulides, D. N.

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

Conti, C.

Crasovan, L.-C.

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Derrien, F.

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, J. Opt. A Pure Appl. Opt. 2, 332 (2000).
[CrossRef]

Edmundson, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Firth, W. J.

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

Fraiman, G. M.

A. G. Litvak, V. A. Mironov, G. M. Fraiman, and A. D. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).

Glorieux, P.

G. Agez, P. Glorieux, C. Szwaj, and E. Louvergneaux, Opt. Commun. 245, 243 (2005).
[CrossRef]

Haelterman, M.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Henninot, J. F.

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, J. Opt. A Pure Appl. Opt. 2, 332 (2000).
[CrossRef]

Hutsebaut, X.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Kartashov, Y. V.

Z. Y. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 12, 2831 (2004).
[CrossRef] [PubMed]

Kivshar, Y. S.

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

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

Kolchugina, I. A.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980)I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , [JETP Lett. 31, 304 (1980)].

Krolikowski, W.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, Phys. Rev. E 68, 036614 (2003).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
[CrossRef]

W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2001).
[CrossRef]

Lederer, F.

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Litvak, A. G.

A. G. Litvak, V. A. Mironov, G. M. Fraiman, and A. D. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).

Louvergneaux, E.

G. Agez, P. Glorieux, C. Szwaj, and E. Louvergneaux, Opt. Commun. 245, 243 (2005).
[CrossRef]

Mamaev, A. V.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Mazilu, D.

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Mezentsev, V. K.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Mihalache, D.

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Mironov, V. A.

V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , Dokl. Akad. Nauk SSSR 260, 325 (1981)V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , [Sov. Phys. Dokl. 26, 861 (1981)].

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980)I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , [JETP Lett. 31, 304 (1980)].

A. G. Litvak, V. A. Mironov, G. M. Fraiman, and A. D. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).

Mitchell, M.

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

Neshev, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, Phys. Rev. E 68, 036614 (2003).
[CrossRef]

Neyts, K.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Nikolov, N. I.

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, Phys. Rev. E 68, 036614 (2003).
[CrossRef]

Ostrovskaya, E. A.

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

Peccianti, M.

Rasmussen, J. J.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Saffman, M.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Sangarpaul, A.

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

Segev, M.

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

Sergeev, A. M.

V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , Dokl. Akad. Nauk SSSR 260, 325 (1981)V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , [Sov. Phys. Dokl. 26, 861 (1981)].

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980)I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , [JETP Lett. 31, 304 (1980)].

Sher, E. M.

V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , Dokl. Akad. Nauk SSSR 260, 325 (1981)V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , [Sov. Phys. Dokl. 26, 861 (1981)].

Skryabin, D. V.

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

Szwaj, C.

G. Agez, P. Glorieux, C. Szwaj, and E. Louvergneaux, Opt. Commun. 245, 243 (2005).
[CrossRef]

Torner, L.

Z. Y. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 12, 2831 (2004).
[CrossRef] [PubMed]

Vysloukh, V. A.

Warenghem, M.

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, J. Opt. A Pure Appl. Opt. 2, 332 (2000).
[CrossRef]

Wyller, J.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Xie, K.

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

Xu, Z. Y.

Z. Y. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef]

Yunakovskii, A. D.

A. G. Litvak, V. A. Mironov, G. M. Fraiman, and A. D. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).

Zozulya, A. A.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Dokl. Akad. Nauk SSSR (1)

V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , Dokl. Akad. Nauk SSSR 260, 325 (1981)V. A. Mironov, A. M. Sergeev, and E. M. Sher, , and , [Sov. Phys. Dokl. 26, 861 (1981)].

J. Opt. A Pure Appl. Opt. (1)

F. Derrien, J. F. Henninot, M. Warenghem, and G. Abbate, J. Opt. A Pure Appl. Opt. 2, 332 (2000).
[CrossRef]

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

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Opt. Commun. (2)

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

G. Agez, P. Glorieux, C. Szwaj, and E. Louvergneaux, Opt. Commun. 245, 243 (2005).
[CrossRef]

Opt. Eng. (1)

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (2)

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Phys. Rev. E (3)

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, Phys. Rev. E 68, 036614 (2003).
[CrossRef]

W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2001).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Phys. Rev. Lett. (3)

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[CrossRef]

Z. Y. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef]

Pis'ma Zh. Eksp. Teor. Fiz. (1)

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980)I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, , and , [JETP Lett. 31, 304 (1980)].

Sov. J. Plasma Phys. (1)

A. G. Litvak, V. A. Mironov, G. M. Fraiman, and A. D. Yunakovskii, Sov. J. Plasma Phys. 1, 31 (1975).

Other (2)

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, arXiv.org, e-print archive, physics/0504003, April 20, 2005.

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

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Figures (4)

Fig. 1
Fig. 1

(a) Profile of a ground-state soliton that corresponds to the points marked by circles in (b) the dispersion diagram and (c) the Hamiltonian-energy diagram.

Fig. 2
Fig. 2

(a) Profile of a dipole-mode soliton that corresponds to the points marked by circles in (b) the dispersion diagram and (c) the Hamiltonian-energy diagram. (d) Profile of a low-energy dipole-mode soliton that corresponds to b = 0.13 at d = 5 .

Fig. 3
Fig. 3

(a) Profile of a triple-mode soliton at b = 1.5 and d = 5 . (b) Real part of the perturbation growth rate for the triple-mode soliton versus a propagation constant. (c) Profile of a quadrupole-mode soliton at b = 2 and d = 5 . (d) Real part of the perturbation growth rate for 1, triple- and 2, quadrupole-mode solitons versus propagation constant at d = 5 . (e) Profile of a fifth-order soliton at b = 2 and d = 8 . (f) Real part of the perturbation growth rate for the fifth-order soliton at d = 8 .

Fig. 4
Fig. 4

Stable propagation of (a) dipole-mode and (b) triple-mode solitons that correspond to b = 1.5 and d = 5 in the presence of white input noise with variance σ noise 2 = 0.01 .

Equations (5)

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i q ξ = 1 2 2 q η 2 q n ,
n d 2 n η 2 = q 2 ,
H = [ 1 2 q η 2 1 2 q 2 G ( η λ ) q ( λ ) 2 d λ ] d η ,
δ u = 1 2 d 2 v d η 2 + b v n v ,
δ v = 1 2 d 2 u d η 2 b u + n u + w Δ n ,

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