Abstract

We demonstrate that modulation of the local strength of the cubic self-focusing (SF) nonlinearity in the two-dimensional geometry, in the form of a circle with contrast Δg of the SF coefficient relative to the ambient medium with a weaker nonlinearity, stabilizes a family of fundamental solitons against the critical collapse. The result is obtained in an analytical form, using the variational approximation and Vakhitov-Kolokolov stability criterion, and corroborated by numerical computations. For the small contrast, the stability interval of the soliton’s norm scales as ΔNΔg (the replacement of the circle by an annulus leads to a reduction of the stability region by perturbations breaking the axial symmetry). To further illustrate this mechanism, we demonstrate, in an exact form, the stabilization of one-dimensional solitons against the critical collapse under the action of a locally enhanced quintic SF nonlinearity.

© 2012 Optical Society of America

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  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, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
    [CrossRef]
  3. Y. Kominis, Phys. Rev. E 73, 066619 (2006).
    [CrossRef]
  4. K. Hizanidis, Y. Kominis, and N. K. Efremidis, Opt. Express 16, 18296 (2008).
    [CrossRef]
  5. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
    [CrossRef]
  6. A. Shapira, N. Voloch-Bloch, B. A. Malomed, and A. Arie, J. Opt. Soc. Am. B 28, 1481 (2011).
    [CrossRef]
  7. J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
    [CrossRef]
  8. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
    [CrossRef]
  9. F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
  10. G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
    [CrossRef]
  11. J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
    [CrossRef]
  12. F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
    [CrossRef]
  13. J. Belmonte-Beitia, V. V. Konotop, V. M. Pérez-García, and V. E. Vekslerchik, Chaos Solitons Fractals 41, 1158 (2009).
  14. L.-C. Qian, M. L. Wall, S. Zhang, Z. Zhou, and H. Pu, Phys. Rev. A 77, 013611 (2008).
    [CrossRef]
  15. T. Mayteevarunyoo, B. A. Malomed, and G. Dong, Phys. Rev. A 78, 053601 (2008).
    [CrossRef]
  16. Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
    [CrossRef]
  17. S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, J. Phys. B 39, 847 (2006).
    [CrossRef]
  18. J. Zeng and B. A. Malomed, Phys. Rev. A 85, 023824 (2012).
  19. V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973).
  20. E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
    [CrossRef]
  21. L. Bergé, Phys. Rep. 303, 259 (1998).
    [CrossRef]
  22. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
    [CrossRef]
  23. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 770 (2009).
    [CrossRef]
  24. N. V. Hung, P. Ziń, M. Trippenbach, and B. A. Malomed, Phys. Rev. E 82, 046602 (2010).
    [CrossRef]
  25. O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Optical Sciences Center Newsletter (2011), Vol. 36, p. 3088.
  26. Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, Opt. Lett. 36, 82 (2011).
    [CrossRef]
  27. M. Vakhitov and A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
    [CrossRef]
  28. M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. B 8, 2082 (1991).
    [CrossRef]
  29. F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, Phys. Rev. A 67, 013605 (2003).
    [CrossRef]
  30. H. Saito and M. Ueda, Phys. Rev. Lett. 90, 040403 (2003).
    [CrossRef]
  31. M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).
  32. F. Kh. Abdullaev and M. Salerno, Phys. Rev. A 72, 033617 (2005).
  33. G. L. Alfimov, V. V. Konotop, and P. Pacciani, Phys. Rev. A 75, 023624 (2007).
    [CrossRef]
  34. E. L. Falcão-Filho, C. B. de Araújo, and J. J. Rodrigues, J. Opt. Soc. Am. B 24, 2948 (2007).
    [CrossRef]

2012 (1)

J. Zeng and B. A. Malomed, Phys. Rev. A 85, 023824 (2012).

2011 (3)

2010 (1)

N. V. Hung, P. Ziń, M. Trippenbach, and B. A. Malomed, Phys. Rev. E 82, 046602 (2010).
[CrossRef]

2009 (2)

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

J. Belmonte-Beitia, V. V. Konotop, V. M. Pérez-García, and V. E. Vekslerchik, Chaos Solitons Fractals 41, 1158 (2009).

2008 (6)

L.-C. Qian, M. L. Wall, S. Zhang, Z. Zhou, and H. Pu, Phys. Rev. A 77, 013611 (2008).
[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, Phys. Rev. A 78, 053601 (2008).
[CrossRef]

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

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

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

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

2007 (3)

G. L. Alfimov, V. V. Konotop, and P. Pacciani, Phys. Rev. A 75, 023624 (2007).
[CrossRef]

E. L. Falcão-Filho, C. B. de Araújo, and J. J. Rodrigues, J. Opt. Soc. Am. B 24, 2948 (2007).
[CrossRef]

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

2006 (5)

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

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, J. Phys. B 39, 847 (2006).
[CrossRef]

Y. Kominis, Phys. Rev. E 73, 066619 (2006).
[CrossRef]

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).

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

2005 (4)

F. Kh. Abdullaev and M. Salerno, Phys. Rev. A 72, 033617 (2005).

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).

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

2003 (3)

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

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, Phys. Rev. A 67, 013605 (2003).
[CrossRef]

H. Saito and M. Ueda, Phys. Rev. Lett. 90, 040403 (2003).
[CrossRef]

1998 (1)

L. Bergé, Phys. Rep. 303, 259 (1998).
[CrossRef]

1991 (1)

1986 (1)

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

1973 (2)

M. Vakhitov and A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973).

Abdullaev, F. K.

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).

Abdullaev, F. Kh.

F. Kh. Abdullaev and M. Salerno, Phys. Rev. A 72, 033617 (2005).

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, Phys. Rev. A 67, 013605 (2003).
[CrossRef]

Alfimov, G. L.

G. L. Alfimov, V. V. Konotop, and P. Pacciani, Phys. Rev. A 75, 023624 (2007).
[CrossRef]

Anderson, D.

Arie, A.

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. V. Konotop, V. M. Pérez-García, and V. E. Vekslerchik, Chaos Solitons Fractals 41, 1158 (2009).

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

Bergé, L.

L. Bergé, Phys. Rep. 303, 259 (1998).
[CrossRef]

Borovkova, O. V.

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Optical Sciences Center Newsletter (2011), Vol. 36, p. 3088.

Caputo, J. G.

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, Phys. Rev. A 67, 013605 (2003).
[CrossRef]

Centurion, M.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).

Christodoulides, D. N.

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

de Araújo, C. B.

Desaix, M.

Dong, G.

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, Phys. Rev. A 78, 053601 (2008).
[CrossRef]

Efremidis, N. K.

Falcão-Filho, E. L.

Fibich, G.

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]

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).

Ghanbari, S.

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, J. Phys. B 39, 847 (2006).
[CrossRef]

Hannaford, P.

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, J. Phys. B 39, 847 (2006).
[CrossRef]

Hizanidis, K.

Hukriede, J.

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

Hung, N. V.

N. V. Hung, P. Ziń, M. Trippenbach, and B. A. Malomed, Phys. Rev. E 82, 046602 (2010).
[CrossRef]

Kartashov, Y. V.

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

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, Opt. Lett. 36, 82 (2011).
[CrossRef]

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, Opt. Lett. 33, 1747 (2008).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Optical Sciences Center Newsletter (2011), Vol. 36, p. 3088.

Kevrekidis, P. G.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).

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

Kieu, T. D.

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, J. Phys. B 39, 847 (2006).
[CrossRef]

Kip, D.

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

Kolokolov, A.

M. Vakhitov and A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Kominis, Y.

Konotop, V. V.

Y. V. Kartashov, V. V. Konotop, and V. A. Vysloukh, Opt. Lett. 36, 82 (2011).
[CrossRef]

J. Belmonte-Beitia, V. V. Konotop, V. M. Pérez-García, and V. E. Vekslerchik, Chaos Solitons Fractals 41, 1158 (2009).

G. L. Alfimov, V. V. Konotop, and P. Pacciani, Phys. Rev. A 75, 023624 (2007).
[CrossRef]

Kraenkel, R. A.

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, Phys. Rev. A 67, 013605 (2003).
[CrossRef]

Kuznetsov, E. A.

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

Lederer, F.

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

Lisak, M.

Malomed, B. A.

J. Zeng and B. A. Malomed, Phys. Rev. A 85, 023824 (2012).

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

A. Shapira, N. Voloch-Bloch, B. A. Malomed, and A. Arie, J. Opt. Soc. Am. B 28, 1481 (2011).
[CrossRef]

N. V. Hung, P. Ziń, M. Trippenbach, and B. A. Malomed, Phys. Rev. E 82, 046602 (2010).
[CrossRef]

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

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, Phys. Rev. A 78, 053601 (2008).
[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]

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, Phys. Rev. A 67, 013605 (2003).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Optical Sciences Center Newsletter (2011), Vol. 36, p. 3088.

Mayteevarunyoo, T.

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, Phys. Rev. A 78, 053601 (2008).
[CrossRef]

Pacciani, P.

G. L. Alfimov, V. V. Konotop, and P. Pacciani, Phys. Rev. A 75, 023624 (2007).
[CrossRef]

Pérez-García, V. M.

J. Belmonte-Beitia, V. V. Konotop, V. M. Pérez-García, and V. E. Vekslerchik, Chaos Solitons Fractals 41, 1158 (2009).

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

Porter, M. A.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).

Psaltis, D.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).

Pu, H.

L.-C. Qian, M. L. Wall, S. Zhang, Z. Zhou, and H. Pu, Phys. Rev. A 77, 013611 (2008).
[CrossRef]

Qian, L.-C.

L.-C. Qian, M. L. Wall, S. Zhang, Z. Zhou, and H. Pu, Phys. Rev. A 77, 013611 (2008).
[CrossRef]

Rodrigues, J. J.

Rubenchik, A. M.

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973).

Runde, D.

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

Saito, H.

H. Saito and M. Ueda, Phys. Rev. Lett. 90, 040403 (2003).
[CrossRef]

Sakaguchi, H.

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]

Salerno, M.

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

F. Kh. Abdullaev and M. Salerno, Phys. Rev. A 72, 033617 (2005).

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]

Shapira, A.

Sidorov, A.

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, J. Phys. B 39, 847 (2006).
[CrossRef]

Silberberg, Y.

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

Sivan, Y.

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

Tomio, L.

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

Torner, L.

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]

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

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Optical Sciences Center Newsletter (2011), Vol. 36, p. 3088.

Torres, P. J.

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

Trippenbach, M.

N. V. Hung, P. Ziń, M. Trippenbach, and B. A. Malomed, Phys. Rev. E 82, 046602 (2010).
[CrossRef]

Ueda, M.

H. Saito and M. Ueda, Phys. Rev. Lett. 90, 040403 (2003).
[CrossRef]

Vakhitov, M.

M. Vakhitov and A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Vekslerchik, V.

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

Vekslerchik, V. E.

J. Belmonte-Beitia, V. V. Konotop, V. M. Pérez-García, and V. E. Vekslerchik, Chaos Solitons Fractals 41, 1158 (2009).

Voloch-Bloch, N.

Vysloukh, V. A.

Wall, M. L.

L.-C. Qian, M. L. Wall, S. Zhang, Z. Zhou, and H. Pu, Phys. Rev. A 77, 013611 (2008).
[CrossRef]

Weinstein, M. I.

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

Zakharov, V. E.

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973).

Zeng, J.

J. Zeng and B. A. Malomed, Phys. Rev. A 85, 023824 (2012).

Zhang, S.

L.-C. Qian, M. L. Wall, S. Zhang, Z. Zhou, and H. Pu, Phys. Rev. A 77, 013611 (2008).
[CrossRef]

Zhou, Z.

L.-C. Qian, M. L. Wall, S. Zhang, Z. Zhou, and H. Pu, Phys. Rev. A 77, 013611 (2008).
[CrossRef]

Zin, P.

N. V. Hung, P. Ziń, M. Trippenbach, and B. A. Malomed, Phys. Rev. E 82, 046602 (2010).
[CrossRef]

Chaos Solitons Fractals (1)

J. Belmonte-Beitia, V. V. Konotop, V. M. Pérez-García, and V. E. Vekslerchik, Chaos Solitons Fractals 41, 1158 (2009).

J. Opt. Soc. Am. B (3)

J. Phys. B (1)

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, J. Phys. B 39, 847 (2006).
[CrossRef]

J. Phys. D (1)

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

Opt. Express (1)

Opt. Lett. (3)

Phys. Rep. (3)

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

L. Bergé, Phys. Rep. 303, 259 (1998).
[CrossRef]

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

Phys. Rev. A (9)

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

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

J. Zeng and B. A. Malomed, Phys. Rev. A 85, 023824 (2012).

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

L.-C. Qian, M. L. Wall, S. Zhang, Z. Zhou, and H. Pu, Phys. Rev. A 77, 013611 (2008).
[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, Phys. Rev. A 78, 053601 (2008).
[CrossRef]

F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, Phys. Rev. A 67, 013605 (2003).
[CrossRef]

F. Kh. Abdullaev and M. Salerno, Phys. Rev. A 72, 033617 (2005).

G. L. Alfimov, V. V. Konotop, and P. Pacciani, Phys. Rev. A 75, 023624 (2007).
[CrossRef]

Phys. Rev. E (4)

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

N. V. Hung, P. Ziń, M. Trippenbach, and B. A. Malomed, Phys. Rev. E 82, 046602 (2010).
[CrossRef]

Y. Kominis, Phys. Rev. E 73, 066619 (2006).
[CrossRef]

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

Phys. Rev. Lett. (4)

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

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

H. Saito and M. Ueda, Phys. Rev. Lett. 90, 040403 (2003).
[CrossRef]

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).

Radiophys. Quantum Electron. (1)

M. Vakhitov and A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Rev. Mod. Phys. (1)

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

Zh. Eksp. Teor. Fiz. (1)

V. E. Zakharov and A. M. Rubenchik, Zh. Eksp. Teor. Fiz. 65, 997 (1973).

Other (1)

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Optical Sciences Center Newsletter (2011), Vol. 36, p. 3088.

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Figures (2)

Fig. 1.
Fig. 1.

(a) Stable localized solution for Δg=0.5, ρ=0 and μ=0.197, N=5.73. (b) The propagation constant of numerically found families of the trapped fundamental modes versus the norm, at fixed values of the nonlinearity contrast between the circle (ρ=0) and surrounding background, Δg=1.5,1,0.5, and 0.1. (c) The same as in (b), but as obtained from the VA.

Fig. 2.
Fig. 2.

(a) Profile of a fundamental soliton trapped in the annulus with ρ=1, Δg=0.5 and μ=0.216, N=9.82. (b) The propagation constant of numerically found families of the trapped modes versus N in annuli with nonlinearity contrast Δg=0.5 and different inner radii ρ. (c) The same as in (b), but as produced by the VA.

Equations (5)

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iϕz=(1/2)2ϕg(r)|ϕ|2ϕ,
g(r)={1,atρ<r<2,1Δg,atr<ρandr>2,.
μu=(1/2)(u+r1u)g(r)u3.
L=2μNNW2+N22πW2[1Δg(1E2+E1)],
(1+e2Δg)1<N/(2π)<1.

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