Abstract

Families of analytical solutions are found for symmetric and antisymmetric solitons in a dual-core system with Kerr nonlinearity and parity-time (PT)-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the “supersymmetric” case, with equal coefficients of gain, loss, and intercore coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching (“management”).

© 2011 Optical Society of America

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  1. C. M. Bender, Rep. Prog. Phys. 70, 947 (2007).
    [CrossRef]
  2. A. Ruschhaupt, F. Delgado, and J. G. Muga, J. Phys. A 38, L171 (2005).
    [CrossRef]
  3. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
    [CrossRef] [PubMed]
  4. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
    [CrossRef] [PubMed]
  5. S. Klaiman, U. Günther, and N. Moiseyev, Phys. Rev. Lett. 101, 080402 (2008).
    [CrossRef] [PubMed]
  6. S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
    [CrossRef] [PubMed]
  7. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Int. J. Theor. Phys. 50, 1019 (2011).
    [CrossRef]
  8. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
    [CrossRef] [PubMed]
  9. C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
    [CrossRef]
  10. A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, Phys. Rev. A 82, 043818 (2010).
    [CrossRef]
  11. H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. ChristodoulidesPhys. Rev. A 82, 043803 (2010).
    [CrossRef]
  12. K. Li and P. G. Kevrekidis, Phys. Rev. E 83, 066608 (2011).
    [CrossRef]
  13. F. Kh. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805(R) (2011).
  14. A. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
    [CrossRef]
  15. S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. A 84, 013833 (2011).
    [CrossRef]
  16. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
    [CrossRef] [PubMed]
  17. B. A. Malomed and H. G. Winful, Phys. Rev. E 53, 5365 (1996).
    [CrossRef]
  18. J. Atai and B. A. Malomed, Phys. Rev. E 54, 4371(1996).
    [CrossRef]
  19. W. J. Firth and P. V. Paulau, Eur. Phys. J. D 59, 13(2010).
    [CrossRef]
  20. A. Marini, D. V. Skryabin, and B. A. Malomed, Opt. Express 19, 6616 (2011).
    [CrossRef] [PubMed]
  21. P. V. Paulau, D. Gomila, P. Colet, N. A. Loiko, N. N. Rosanov, T. Ackemann, and W. J. Firth, Opt. Express 18, 8859(2010).
    [CrossRef] [PubMed]
  22. P. V. Paulau, D. Gomila, P. Colet, B. A. Malomed, and W. J. Firth, Phys. Rev. E 84, 036213 (2011).
    [CrossRef]
  23. E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
    [CrossRef] [PubMed]
  24. A. I. Maimistov, Sov. J. Quantum Electron. 21, 687 (1991).
    [CrossRef]
  25. J. M. Soto-Crespo and N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
    [CrossRef]
  26. P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
    [CrossRef]
  27. R. Driben, B. A. Malomed, and P. L. Chu, J. Opt. Soc. Am. B 20, 2338 (2003).
    [CrossRef]
  28. B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).
  29. C. Li, G. Xu, L. Ma, N. Dou, and H. Gu, J. Opt. A 7, 540 (2005).
    [CrossRef]
  30. Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
    [CrossRef]
  31. K. S. Chiang, Opt. Lett. 20, 997 (1995).
    [CrossRef] [PubMed]

2011 (8)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Int. J. Theor. Phys. 50, 1019 (2011).
[CrossRef]

K. Li and P. G. Kevrekidis, Phys. Rev. E 83, 066608 (2011).
[CrossRef]

F. Kh. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805(R) (2011).

A. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
[CrossRef]

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. A 84, 013833 (2011).
[CrossRef]

A. Marini, D. V. Skryabin, and B. A. Malomed, Opt. Express 19, 6616 (2011).
[CrossRef] [PubMed]

P. V. Paulau, D. Gomila, P. Colet, B. A. Malomed, and W. J. Firth, Phys. Rev. E 84, 036213 (2011).
[CrossRef]

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

2010 (5)

W. J. Firth and P. V. Paulau, Eur. Phys. J. D 59, 13(2010).
[CrossRef]

P. V. Paulau, D. Gomila, P. Colet, N. A. Loiko, N. N. Rosanov, T. Ackemann, and W. J. Firth, Opt. Express 18, 8859(2010).
[CrossRef] [PubMed]

C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, Phys. Rev. A 82, 043818 (2010).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. ChristodoulidesPhys. Rev. A 82, 043803 (2010).
[CrossRef]

2009 (2)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef] [PubMed]

2008 (3)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

S. Klaiman, U. Günther, and N. Moiseyev, Phys. Rev. Lett. 101, 080402 (2008).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

2007 (2)

2005 (2)

A. Ruschhaupt, F. Delgado, and J. G. Muga, J. Phys. A 38, L171 (2005).
[CrossRef]

C. Li, G. Xu, L. Ma, N. Dou, and H. Gu, J. Opt. A 7, 540 (2005).
[CrossRef]

2003 (1)

1996 (2)

B. A. Malomed and H. G. Winful, Phys. Rev. E 53, 5365 (1996).
[CrossRef]

J. Atai and B. A. Malomed, Phys. Rev. E 54, 4371(1996).
[CrossRef]

1995 (1)

1993 (2)

J. M. Soto-Crespo and N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
[CrossRef]

1991 (1)

A. I. Maimistov, Sov. J. Quantum Electron. 21, 687 (1991).
[CrossRef]

1989 (1)

E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
[CrossRef] [PubMed]

Abdullaev, F. Kh.

F. Kh. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805(R) (2011).

Ackemann, T.

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Akhmediev, N.

J. M. Soto-Crespo and N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

Atai, J.

J. Atai and B. A. Malomed, Phys. Rev. E 54, 4371(1996).
[CrossRef]

Bender, C. M.

C. M. Bender, Rep. Prog. Phys. 70, 947 (2007).
[CrossRef]

Chiang, K. S.

Christodoulides, D. N.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Int. J. Theor. Phys. 50, 1019 (2011).
[CrossRef]

C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. ChristodoulidesPhys. Rev. A 82, 043803 (2010).
[CrossRef]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
[CrossRef] [PubMed]

Chu, P. L.

Colet, P.

Delgado, F.

A. Ruschhaupt, F. Delgado, and J. G. Muga, J. Phys. A 38, L171 (2005).
[CrossRef]

Dmitriev, S. V.

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. A 84, 013833 (2011).
[CrossRef]

Dou, N.

C. Li, G. Xu, L. Ma, N. Dou, and H. Gu, J. Opt. A 7, 540 (2005).
[CrossRef]

Driben, R.

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

El-Ganainy, R.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Int. J. Theor. Phys. 50, 1019 (2011).
[CrossRef]

C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. ChristodoulidesPhys. Rev. A 82, 043803 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
[CrossRef] [PubMed]

Firth, W. J.

P. V. Paulau, D. Gomila, P. Colet, B. A. Malomed, and W. J. Firth, Phys. Rev. E 84, 036213 (2011).
[CrossRef]

P. V. Paulau, D. Gomila, P. Colet, N. A. Loiko, N. N. Rosanov, T. Ackemann, and W. J. Firth, Opt. Express 18, 8859(2010).
[CrossRef] [PubMed]

W. J. Firth and P. V. Paulau, Eur. Phys. J. D 59, 13(2010).
[CrossRef]

Gomila, D.

Gu, H.

C. Li, G. Xu, L. Ma, N. Dou, and H. Gu, J. Opt. A 7, 540 (2005).
[CrossRef]

Günther, U.

S. Klaiman, U. Günther, and N. Moiseyev, Phys. Rev. Lett. 101, 080402 (2008).
[CrossRef] [PubMed]

Guo, A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Kartashov, Y. V.

F. Kh. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805(R) (2011).

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

Kevrekidis, P. G.

K. Li and P. G. Kevrekidis, Phys. Rev. E 83, 066608 (2011).
[CrossRef]

Kip, D.

C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Kivshar, Y. S.

A. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
[CrossRef]

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. A 84, 013833 (2011).
[CrossRef]

A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, Phys. Rev. A 82, 043818 (2010).
[CrossRef]

Klaiman, S.

S. Klaiman, U. Günther, and N. Moiseyev, Phys. Rev. Lett. 101, 080402 (2008).
[CrossRef] [PubMed]

Konotop, V. V.

F. Kh. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805(R) (2011).

Kottos, T.

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. ChristodoulidesPhys. Rev. A 82, 043803 (2010).
[CrossRef]

Li, C.

C. Li, G. Xu, L. Ma, N. Dou, and H. Gu, J. Opt. A 7, 540 (2005).
[CrossRef]

Li, K.

K. Li and P. G. Kevrekidis, Phys. Rev. E 83, 066608 (2011).
[CrossRef]

Loiko, N. A.

Longhi, S.

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef] [PubMed]

Ma, L.

C. Li, G. Xu, L. Ma, N. Dou, and H. Gu, J. Opt. A 7, 540 (2005).
[CrossRef]

Maimistov, A. I.

A. I. Maimistov, Sov. J. Quantum Electron. 21, 687 (1991).
[CrossRef]

Makris, K. G.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Int. J. Theor. Phys. 50, 1019 (2011).
[CrossRef]

C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
[CrossRef] [PubMed]

Malomed, B. A.

A. Marini, D. V. Skryabin, and B. A. Malomed, Opt. Express 19, 6616 (2011).
[CrossRef] [PubMed]

A. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
[CrossRef]

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

P. V. Paulau, D. Gomila, P. Colet, B. A. Malomed, and W. J. Firth, Phys. Rev. E 84, 036213 (2011).
[CrossRef]

R. Driben, B. A. Malomed, and P. L. Chu, J. Opt. Soc. Am. B 20, 2338 (2003).
[CrossRef]

J. Atai and B. A. Malomed, Phys. Rev. E 54, 4371(1996).
[CrossRef]

B. A. Malomed and H. G. Winful, Phys. Rev. E 53, 5365 (1996).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
[CrossRef]

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

Marini, A.

Miroshnichenko, A.

A. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
[CrossRef]

Moiseyev, N.

S. Klaiman, U. Günther, and N. Moiseyev, Phys. Rev. Lett. 101, 080402 (2008).
[CrossRef] [PubMed]

Morandotti, R.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Muga, J. G.

A. Ruschhaupt, F. Delgado, and J. G. Muga, J. Phys. A 38, L171 (2005).
[CrossRef]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Int. J. Theor. Phys. 50, 1019 (2011).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
[CrossRef] [PubMed]

Paulau, P. V.

P. V. Paulau, D. Gomila, P. Colet, B. A. Malomed, and W. J. Firth, Phys. Rev. E 84, 036213 (2011).
[CrossRef]

P. V. Paulau, D. Gomila, P. Colet, N. A. Loiko, N. N. Rosanov, T. Ackemann, and W. J. Firth, Opt. Express 18, 8859(2010).
[CrossRef] [PubMed]

W. J. Firth and P. V. Paulau, Eur. Phys. J. D 59, 13(2010).
[CrossRef]

Peng, G. D.

Ramezani, H.

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. ChristodoulidesPhys. Rev. A 82, 043803 (2010).
[CrossRef]

Rosanov, N. N.

Ruschhaupt, A.

A. Ruschhaupt, F. Delgado, and J. G. Muga, J. Phys. A 38, L171 (2005).
[CrossRef]

Ruter, C. E.

C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Salamo, G. J.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Segev, M.

C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Siviloglou, G. A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Skryabin, D. V.

Soto-Crespo, J. M.

J. M. Soto-Crespo and N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

Stegeman, G. I.

E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
[CrossRef] [PubMed]

Suchkov, S. V.

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. A 84, 013833 (2011).
[CrossRef]

Sukhorukov, A. A.

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. A 84, 013833 (2011).
[CrossRef]

A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, Phys. Rev. A 82, 043818 (2010).
[CrossRef]

Torner, L.

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

Volatier-Ravat, M.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Wabnitz, S.

E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
[CrossRef] [PubMed]

Winful, H. G.

B. A. Malomed and H. G. Winful, Phys. Rev. E 53, 5365 (1996).
[CrossRef]

Wright, E. M.

E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
[CrossRef] [PubMed]

Xu, G.

C. Li, G. Xu, L. Ma, N. Dou, and H. Gu, J. Opt. A 7, 540 (2005).
[CrossRef]

Xu, Z.

A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, Phys. Rev. A 82, 043818 (2010).
[CrossRef]

Zezyulin, D. A.

F. Kh. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805(R) (2011).

Eur. Phys. J. D (1)

W. J. Firth and P. V. Paulau, Eur. Phys. J. D 59, 13(2010).
[CrossRef]

Int. J. Theor. Phys. (1)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Int. J. Theor. Phys. 50, 1019 (2011).
[CrossRef]

J. Opt. A (1)

C. Li, G. Xu, L. Ma, N. Dou, and H. Gu, J. Opt. A 7, 540 (2005).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. A (1)

A. Ruschhaupt, F. Delgado, and J. G. Muga, J. Phys. A 38, L171 (2005).
[CrossRef]

Nat. Phys. (1)

C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (6)

A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, Phys. Rev. A 82, 043818 (2010).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. ChristodoulidesPhys. Rev. A 82, 043803 (2010).
[CrossRef]

F. Kh. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, Phys. Rev. A 83, 041805(R) (2011).

A. Miroshnichenko, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 84, 012123 (2011).
[CrossRef]

S. V. Dmitriev, S. V. Suchkov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. A 84, 013833 (2011).
[CrossRef]

E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
[CrossRef] [PubMed]

Phys. Rev. E (5)

J. M. Soto-Crespo and N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

P. V. Paulau, D. Gomila, P. Colet, B. A. Malomed, and W. J. Firth, Phys. Rev. E 84, 036213 (2011).
[CrossRef]

B. A. Malomed and H. G. Winful, Phys. Rev. E 53, 5365 (1996).
[CrossRef]

J. Atai and B. A. Malomed, Phys. Rev. E 54, 4371(1996).
[CrossRef]

K. Li and P. G. Kevrekidis, Phys. Rev. E 83, 066608 (2011).
[CrossRef]

Phys. Rev. Lett. (5)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

S. Klaiman, U. Günther, and N. Moiseyev, Phys. Rev. Lett. 101, 080402 (2008).
[CrossRef] [PubMed]

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef] [PubMed]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

C. M. Bender, Rep. Prog. Phys. 70, 947 (2007).
[CrossRef]

Rev. Mod. Phys. (1)

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

Sov. J. Quantum Electron. (1)

A. I. Maimistov, Sov. J. Quantum Electron. 21, 687 (1991).
[CrossRef]

Other (1)

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

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Figures (4)

Fig. 1
Fig. 1

Analytical stability border of Eq. (4) and its numerically found counterpart for the PT -symmetric solitons, and the numerical stability border for the PT - antisymmetric solitons. The solitons with amplitude η are stable at η < η max .

Fig. 2
Fig. 2

Examples of the relaxation of stable perturbed (a)  PT -symmetric and (b) antisymmetric solitons, with γ = 0.5 , η = 0.9 and γ = 0.5 , η = 0.7 , respectively. Here and in the case shown in Fig. 3, the evolution of the v component is similar to what is shown for u ( z , t ) .

Fig. 3
Fig. 3

Elastic collision between stable solitons of the two different types, with η = 0.7 , boosted by frequency shift χ = ± 5 at γ = 0.7 .

Fig. 4
Fig. 4

Self-trapping of the soliton in the supersymmetric system ( Γ = γ = κ = 1 ) subject to the management with period Δ z = 2 . The input is u 0 = i v 0 = 0.9 sech ( t ) .

Equations (5)

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i u z + ( 1 / 2 ) u t t + | u | 2 u i γ u + κ v = 0 , i v z + ( 1 / 2 ) v t t + | v | 2 v + i Γ v + κ u = 0 ,
v = ( i γ ± 1 γ 2 ) u = U ( z , t )
U ( z , t ) = η exp ( i ( η 2 / 2 ± 1 γ 2 ) z ) sech ( η t ) .
η max 2 ( γ ) = ( 4 / 3 ) 1 γ 2 .
L ^ ( δ u + i δ v ) = 0 , L ^ ( δ u i δ v ) = 2 i κ ( δ u + i δ v ) ,

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