Abstract

We consider two-component solitons in a medium with a periodic modulation of the nonlinear coefficient. The modulation enables the existence of complex multihump vector states. In particular, vector solitons composed of dipole and fundamental or dipole and even double-hump components exist and may be stable. Families of unstable scalar solitons can be stabilized in the vectorial form, due to the coupling to a stable second component.

© 2009 Optical Society of America

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  1. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
    [CrossRef]
  2. F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
    [CrossRef]
  3. G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
    [CrossRef]
  4. G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
    [CrossRef]
  5. Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
    [CrossRef] [PubMed]
  6. J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
    [CrossRef] [PubMed]
  7. F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
    [CrossRef]
  8. A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, Phys. Rev. A 78, 013611 (2008).
    [CrossRef]
  9. Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
    [CrossRef]
  10. Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
    [CrossRef]
  11. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
    [CrossRef] [PubMed]
  12. K. Hizanidis, Y. Kominis, and N. K. Efremidis, Opt. Express 16, 18296 (2008).
    [CrossRef] [PubMed]
  13. Y. Kominis and K. Hizanidis, Opt. Express 16, 12124 (2008).
    [CrossRef] [PubMed]
  14. F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
    [CrossRef]
  15. S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
    [CrossRef]
  16. O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
    [CrossRef] [PubMed]
  17. A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
    [CrossRef] [PubMed]
  18. Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
    [CrossRef]
  19. S. K. Adhikari and B. A. Malomed, Phys. Rev. A 77, 023607 (2008).
    [CrossRef]
  20. J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
    [CrossRef] [PubMed]
  21. F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
    [CrossRef]
  22. P. D. Rasmussen, F. H. Bennet, D. N. Neshev, A. A. Sukhorukov, C. R. Rosberg, W. Krolikowski, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 295 (2009).
    [CrossRef] [PubMed]
  23. J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
    [CrossRef]

2009 (1)

2008 (7)

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

Y. Kominis and K. Hizanidis, Opt. Express 16, 12124 (2008).
[CrossRef] [PubMed]

K. Hizanidis, Y. Kominis, and N. K. Efremidis, Opt. Express 16, 18296 (2008).
[CrossRef] [PubMed]

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, Phys. Rev. A 78, 013611 (2008).
[CrossRef]

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

S. K. Adhikari and B. A. Malomed, Phys. Rev. A 77, 023607 (2008).
[CrossRef]

2007 (3)

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

2006 (3)

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[CrossRef]

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

2005 (3)

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
[CrossRef]

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

2004 (1)

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[CrossRef]

2003 (4)

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef] [PubMed]

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

1998 (1)

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Abdullaev, F.

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

Abdullaev, F. K.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
[CrossRef]

Abdumalikov, A.

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

Adhikari, S. K.

S. K. Adhikari and B. A. Malomed, Phys. Rev. A 77, 023607 (2008).
[CrossRef]

Aitchison, J. S.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Bang, O.

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Bennet, F. H.

Bishop, A. R.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, Phys. Rev. A 78, 013611 (2008).
[CrossRef]

Bludov, Y. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[CrossRef]

Christodoulides, D.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Christodoulides, D. N.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

Cohen, O.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

Darmanyan, S.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Dmitriev, S. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Efremidis, N. K.

Fibich, G.

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Fleischer, J. W.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

Frantzeskakis, D. J.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, Phys. Rev. A 78, 013611 (2008).
[CrossRef]

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

Galimzyanov, R.

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

Gammal, A.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Garnier, J.

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
[CrossRef]

Hizanidis, K.

Hudock, J.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Hukriede, J.

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

Jones, C. K. R. T.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[CrossRef]

Kevrekidis, P. G.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, Phys. Rev. A 78, 013611 (2008).
[CrossRef]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

Kip, D.

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

Kivshar, Y. S.

Kobyakov, A.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Kominis, Y.

Konotop, V. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[CrossRef]

Krolikowski, W.

Lederer, F.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Malomed, B. A.

S. K. Adhikari and B. A. Malomed, Phys. Rev. A 77, 023607 (2008).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Meier, J.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Morandotti, R.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Neshev, D. N.

Perez-Garcia, V. M.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Porter, M. A.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, Phys. Rev. A 78, 013611 (2008).
[CrossRef]

Rapti, Z.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Rasmussen, P. D.

Rodrigues, A. S.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, Phys. Rev. A 78, 013611 (2008).
[CrossRef]

Rosberg, C. R.

Runde, D.

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Salerno, M.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Schmelcher, P.

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, Phys. Rev. A 78, 013611 (2008).
[CrossRef]

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

Schmidt, E.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Schwartz, T.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

Segev, M.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Sivan, Y.

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Stegeman, G.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Sukhorukov, A. A.

Theocharis, G.

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

Tomio, L.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[CrossRef]

Torres, P. J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Vekslerchik, V.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[CrossRef]

Weinstein, M. I.

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Zelenina, A. S.

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[CrossRef]

J. Phys. A (1)

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

J. Phys. D (1)

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Lett. A (1)

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

Phys. Rev. A (6)

A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, Phys. Rev. A 78, 013611 (2008).
[CrossRef]

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[CrossRef]

S. K. Adhikari and B. A. Malomed, Phys. Rev. A 77, 023607 (2008).
[CrossRef]

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
[CrossRef]

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Phys. Rev. E (4)

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[CrossRef]

Phys. Rev. Lett. (5)

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef] [PubMed]

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Physica D (1)

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Profiles of fundamental, dipole, and even-shaped scalar solitons with b 1 = 1.5 . In gray regions σ ( η ) < 1 / 2 , while in white ones σ ( η ) > 1 / 2 . (b) Energy flow versus b 1 for the fundamental and even solitons. Circles correspond to the solitons shown in (a).

Fig. 2
Fig. 2

(a) Profile of the fundamental-dipole vector soliton at b 1 = 1.9 , b 2 = 3 . (b) Energy sharing between the components versus b 1 at b 2 = 3 . (c) Energy flow versus b 1 . The circle corresponds to the soliton shown in (a). (d) Existence domain in the ( b 2 , b 1 ) plane. In this figure and Fig. 3 C = 1 , except for Fig. 3e.

Fig. 3
Fig. 3

(a) Profile of the even-dipole vector soliton at b 1 = 2.67 and b 2 = 3 . (b) Energy sharing versus b 1 at b 2 = 3 . (c) Lower cutoff b 1 low for the even-dipole soliton versus b 2 . (d) Stability (white) and instability (shaded) domains in the ( b 1 , b 2 ) plane, and (e) in the ( C , b 1 ) plane at b 2 = 3 . (f) δ r versus b 1 at b 2 = 3 .

Equations (3)

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

i q 1 , 2 ξ = 1 2 2 q 1 , 2 η 2 + σ ( η ) q 1 , 2 ( | q 1 , 2 | 2 + C | q 2 , 1 | 2 ) .
δ u 1 , 2 = 1 2 d 2 v 1 , 2 d η 2 + [ σ ( w 1 , 2 2 + C w 2 , 1 2 ) + b 1 , 2 ] v 1 , 2 ,
δ v 1 , 2 = + 1 2 d 2 u 1 , 2 d η 2 [ σ ( 3 w 1 , 2 2 + C w 2 , 1 2 ) + b 1 , 2 ] u 1 , 2 2 σ C w 1 w 2 u 2 , 1 .

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