Abstract

We show that an inhomogeneous defocusing nonlinearity that grows toward the periphery in the positive and negative transverse directions at different rates can support strongly asymmetric fundamental and multipole bright solitons, which are stable in wide parameter regions. In the limiting case, when nonlinearity is uniform in one direction, solitons transform into stable domain walls (fronts), with constant or oscillating intensity in the homogeneous region, attached to a tail rapidly decaying in the direction of growing nonlinearity.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
    [CrossRef]
  2. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
    [CrossRef]
  3. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef]
  4. Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
    [CrossRef]
  5. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
    [CrossRef]
  6. F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
    [CrossRef]
  7. G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
    [CrossRef]
  8. J. Garnier and F. K. Abdullaev, Phys. Rev. A 74, 013604 (2006).
    [CrossRef]
  9. G. Fibich, Y. Sivan, and M. I. Weinstein, Phys. D 217, 31 (2006).
    [CrossRef]
  10. Y. Kominis and K. Hizanidis, Opt. Lett. 31, 2888 (2006).
    [CrossRef]
  11. Y. Kominis and K. Hizanidis, Opt. Express 16, 12124 (2008).
    [CrossRef]
  12. F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
    [CrossRef]
  13. J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
    [CrossRef]
  14. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
    [CrossRef]
  15. Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
    [CrossRef]
  16. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 770 (2009).
    [CrossRef]
  17. H. Sakaguchi and B. A. Malomed, Opt. Lett. 37, 1035 (2012).
    [CrossRef]
  18. O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
    [CrossRef]
  19. O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Phys. Rev. E 84, 035602(R) (2011).
    [CrossRef]
  20. Q. Tian, L. Wu, Y. Zhang, and J. F. Zhang, Phys. Rev. E 85, 056603 (2012).
    [CrossRef]
  21. J. Zeng and B. A. Malomed, Phys. Rev. E 86, 036607 (2012).
    [CrossRef]
  22. S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vazquez, Phys. Rev. B 59, 5994 (1999).
    [CrossRef]
  23. E. Smirnov, C. E. Rüter, D. Kip, Y. V. Kartashov, and L. Torner, Opt. Lett. 32, 1950 (2007).
    [CrossRef]
  24. F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 106, 093901 (2011).
    [CrossRef]
  25. Y. Kominis, A. Papadopoulos, and K. Hizanidis, Opt. Express 15, 10041 (2007).
    [CrossRef]

2012 (3)

H. Sakaguchi and B. A. Malomed, Opt. Lett. 37, 1035 (2012).
[CrossRef]

Q. Tian, L. Wu, Y. Zhang, and J. F. Zhang, Phys. Rev. E 85, 056603 (2012).
[CrossRef]

J. Zeng and B. A. Malomed, Phys. Rev. E 86, 036607 (2012).
[CrossRef]

2011 (4)

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 106, 093901 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Phys. Rev. E 84, 035602(R) (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

2009 (2)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 770 (2009).
[CrossRef]

2008 (3)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Y. Kominis and K. Hizanidis, Opt. Express 16, 12124 (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]

2007 (3)

2006 (5)

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

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

J. Garnier and F. K. Abdullaev, Phys. Rev. A 74, 013604 (2006).
[CrossRef]

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

Y. Kominis and K. Hizanidis, Opt. Lett. 31, 2888 (2006).
[CrossRef]

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]

2001 (1)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

1999 (1)

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vazquez, Phys. Rev. B 59, 5994 (1999).
[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]

J. Garnier and F. K. Abdullaev, Phys. Rev. A 74, 013604 (2006).
[CrossRef]

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

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Alexander, T. J.

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 106, 093901 (2011).
[CrossRef]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Belmonte-Beitia, J.

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

Bennet, F. H.

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 106, 093901 (2011).
[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]

Borovkova, O. V.

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Phys. Rev. E 84, 035602(R) (2011).
[CrossRef]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Darmanyan, S.

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vazquez, Phys. Rev. B 59, 5994 (1999).
[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]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Fibich, G.

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

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

Frantzeskakis, D. J.

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

Garnier, J.

J. Garnier and F. K. Abdullaev, Phys. Rev. A 74, 013604 (2006).
[CrossRef]

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

Haslinger, F.

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 106, 093901 (2011).
[CrossRef]

Hizanidis, K.

Kartashov, Y. V.

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Phys. Rev. E 84, 035602(R) (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 770 (2009).
[CrossRef]

E. Smirnov, C. E. Rüter, D. Kip, Y. V. Kartashov, and L. Torner, Opt. Lett. 32, 1950 (2007).
[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]

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

Kip, D.

Kivshar, Y. S.

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 106, 093901 (2011).
[CrossRef]

Kobyakov, A.

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vazquez, Phys. Rev. B 59, 5994 (1999).
[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]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vazquez, Phys. Rev. B 59, 5994 (1999).
[CrossRef]

Malomed, B. A.

H. Sakaguchi and B. A. Malomed, Opt. Lett. 37, 1035 (2012).
[CrossRef]

J. Zeng and B. A. Malomed, Phys. Rev. E 86, 036607 (2012).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Phys. Rev. E 84, 035602(R) (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 770 (2009).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

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

Mitchell, A.

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 106, 093901 (2011).
[CrossRef]

Morandotti, R.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Neshev, D. N.

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 106, 093901 (2011).
[CrossRef]

Papadopoulos, A.

Perez-Garcia, V. M.

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

Rüter, C. E.

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, Opt. Lett. 37, 1035 (2012).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

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

Schmelcher, P.

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

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Sivan, Y.

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

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

Smirnov, E.

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Theocharis, G.

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

Tian, Q.

Q. Tian, L. Wu, Y. Zhang, and J. F. Zhang, Phys. Rev. E 85, 056603 (2012).
[CrossRef]

Torner, L.

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Phys. Rev. E 84, 035602(R) (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 770 (2009).
[CrossRef]

E. Smirnov, C. E. Rüter, D. Kip, Y. V. Kartashov, and L. Torner, Opt. Lett. 32, 1950 (2007).
[CrossRef]

Torres, P. J.

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

Vazquez, L.

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vazquez, Phys. Rev. B 59, 5994 (1999).
[CrossRef]

Vekslerchik, V.

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

Vysloukh, V. A.

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 770 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

Weinstein, M. I.

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

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

Wu, L.

Q. Tian, L. Wu, Y. Zhang, and J. F. Zhang, Phys. Rev. E 85, 056603 (2012).
[CrossRef]

Zeng, J.

J. Zeng and B. A. Malomed, Phys. Rev. E 86, 036607 (2012).
[CrossRef]

Zhang, J. F.

Q. Tian, L. Wu, Y. Zhang, and J. F. Zhang, Phys. Rev. E 85, 056603 (2012).
[CrossRef]

Zhang, Y.

Q. Tian, L. Wu, Y. Zhang, and J. F. Zhang, Phys. Rev. E 85, 056603 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. D (1)

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

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Phys. Rev. A (3)

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]

J. Garnier and F. K. Abdullaev, Phys. Rev. A 74, 013604 (2006).
[CrossRef]

Phys. Rev. B (1)

S. Darmanyan, A. Kobyakov, F. Lederer, and L. Vazquez, Phys. Rev. B 59, 5994 (1999).
[CrossRef]

Phys. Rev. E (6)

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

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Phys. Rev. E 84, 035602(R) (2011).
[CrossRef]

Q. Tian, L. Wu, Y. Zhang, and J. F. Zhang, Phys. Rev. E 85, 056603 (2012).
[CrossRef]

J. Zeng and B. A. Malomed, Phys. Rev. E 86, 036607 (2012).
[CrossRef]

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

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

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

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

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef]

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 106, 093901 (2011).
[CrossRef]

Prog. Opt. (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

Rev. Mod. Phys. (1)

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Stable fundamental and dipole solitons at b=10 for αl=1 (curves 1) and αl=0.1 (curves 2). (b) Stable tripole solitons at αl=0.1 for b=5 (curve 1) and b=20 (curve 2). Nonlinearity landscapes σ(η) are shown for αl=0.1.

Fig. 2.
Fig. 2.

(a) Energy flow versus αl for fundamental (k=0) and dipole (k=1) solitons at b=10. Circles correspond to solitons in Fig. 1(a). (b) Energy flow versus b for tripole (k=2) solitons at αl=0.1 (curve 1) and αl=0.4 (curve 2). A short red segment of curve 1 correspond to unstable tripoles. Circles correspond to solitons in Fig. 1(b). (c) Domains of stability (white) and instability (shaded) for tripole solitons.

Fig. 3.
Fig. 3.

Evolution of unstable (a) and stable (b) tripoles with b=4 and b=6, respectively, and αl=0.1.

Fig. 4.
Fig. 4.

(a) Renormalized energy flow of the DWs versus the propagation constant for αl=0. (b) The profile of the DW with b=2 (the black line) corresponding to the circle in (a). The solution with the c-noidal-wave form at η<0 is shown by the green curve, also for b=2.

Fig. 5.
Fig. 5.

Stable propagation of a DW (a) and solution with the c-noidal-wave form at η<0 (b) in the presence of initial noise. Both solutions correspond to b=2.

Equations (3)

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

iqξ=122qη2+σ(η)q|q|2,
w(η)={21/2ηexp(η2/2),atη0,w0sn(βη,κ),atη<0,
w(η)={31/2sinh(η)sech2(η),atη0,w0sn(βη,κ),atη<0,

Metrics