Abstract

We investigate properties of dark solitons under competing nonlocal cubic–local quintic nonlinearities. Analytical results, based on a variational approach and confirmed by direct numerical simulations, reveal the existence of a unique dark soliton solutions with their width being independent of the degree of nonlocality, due to the competing cubic–quintic nonlinearities.

© 2012 Optical Society of America

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    [CrossRef]
  2. S. Skupin, M. Saffman, and W. Krolikowski, Phys. Rev. Lett. 98, 263902 (2007).
    [CrossRef]
  3. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
    [CrossRef]
  4. P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
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  5. Y. V. Kartashov and L. Torner, Opt. Lett. 32, 946 (2007).
    [CrossRef]
  6. Y. Y. Lin and R.-K. Lee, Opt. Express 15, 8781 (2007).
    [CrossRef]
  7. S. Ouyang and Q. Guo, Opt. Express 17, 5170 (2009).
    [CrossRef]
  8. Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Opt. Lett. 35, 2152 (2010).
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  9. A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
    [CrossRef]
  10. Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Phys. Rev. A 82, 013826 (2010).
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    [CrossRef]
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    [CrossRef]
  18. K.-H. Kuo, Y. Y. Lin, R.-K. Lee, and B. A. Malomed, Phys. Rev. A 83, 053838 (2011).
    [CrossRef]
  19. Z. Zhou, Y. Du, C. Hou, H. Tian, and Y. Wang, J. Opt. Soc. Am. B 28, 1583 (2011).
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  20. E. N. Tsoy, Phys. Rev. A 82, 063829 (2010).
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    [CrossRef]
  22. S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
    [CrossRef]
  23. B. B. Baizakov, F. Kh Abdullaev, B. A. Malomed, and M. Salerno, J. Phys. B 42, 175302 (2009).
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  24. Yu. A. Zaliznyak and A. I. Yakimenko, Phys. Lett. A 372, 2862 (2008).
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  25. S.-Z. Pu, C.-F. Hou, K.-Y. Zhan, C.-X. Yuan, and Y.-W. Du, Opt. Commun. 285, 3631 (2012).
    [CrossRef]
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  27. M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
    [CrossRef]
  28. W.-P. Zhong and M. Belić, Phys. Rev. A 79, 023804 (2009).
    [CrossRef]

2012

S.-Z. Pu, C.-F. Hou, K.-Y. Zhan, C.-X. Yuan, and Y.-W. Du, Opt. Commun. 285, 3631 (2012).
[CrossRef]

2011

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

B. K. Esbensen, A. Wlotzka, M. Bache, O. Bang, and W. Krolikowski, Phys. Rev. A 84, 053854 (2011).
[CrossRef]

Y. Du, Z. Zhou, H. Tian, and D. Liu, J. Opt. 13, 015201 (2011).
[CrossRef]

K.-H. Kuo, Y. Y. Lin, R.-K. Lee, and B. A. Malomed, Phys. Rev. A 83, 053838 (2011).
[CrossRef]

Z. Zhou, Y. Du, C. Hou, H. Tian, and Y. Wang, J. Opt. Soc. Am. B 28, 1583 (2011).
[CrossRef]

2010

E. N. Tsoy, Phys. Rev. A 82, 063829 (2010).
[CrossRef]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Phys. Rev. A 82, 013826 (2010).
[CrossRef]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Opt. Lett. 35, 2152 (2010).
[CrossRef]

2009

S. Ouyang and Q. Guo, Opt. Express 17, 5170 (2009).
[CrossRef]

W.-P. Zhong and M. Belić, Phys. Rev. A 79, 023804 (2009).
[CrossRef]

B. B. Baizakov, F. Kh Abdullaev, B. A. Malomed, and M. Salerno, J. Phys. B 42, 175302 (2009).
[CrossRef]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 79, 013803 (2009).
[CrossRef]

2008

Yu. A. Zaliznyak and A. I. Yakimenko, Phys. Lett. A 372, 2862 (2008).
[CrossRef]

M. Warenghem, J. F. Blach, and J. F. Henninot, J. Opt. Soc. Am. B 25, 1882 (2008).
[CrossRef]

2007

2006

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef]

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, Phys. Rev. Lett. 97, 250402 (2006).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, L. C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

2005

P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef]

1995

Yu. S. Kivshar and W. Krolikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

1992

J. Herrmann, Opt. Commun. 91, 337 (1992).
[CrossRef]

Abdullaev, F. Kh

B. B. Baizakov, F. Kh Abdullaev, B. A. Malomed, and M. Salerno, J. Phys. B 42, 175302 (2009).
[CrossRef]

Alfassi, B.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Assanto, G.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Bache, M.

B. K. Esbensen, A. Wlotzka, M. Bache, O. Bang, and W. Krolikowski, Phys. Rev. A 84, 053854 (2011).
[CrossRef]

Baizakov, B. B.

B. B. Baizakov, F. Kh Abdullaev, B. A. Malomed, and M. Salerno, J. Phys. B 42, 175302 (2009).
[CrossRef]

Bang, O.

B. K. Esbensen, A. Wlotzka, M. Bache, O. Bang, and W. Krolikowski, Phys. Rev. A 84, 053854 (2011).
[CrossRef]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Opt. Lett. 35, 2152 (2010).
[CrossRef]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Phys. Rev. A 82, 013826 (2010).
[CrossRef]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

Belic, M.

W.-P. Zhong and M. Belić, Phys. Rev. A 79, 023804 (2009).
[CrossRef]

Blach, J. F.

Burgess, I. B.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

Cohen, O.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Crasovan, L. C.

D. Mihalache, D. Mazilu, F. Lederer, L. C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Crosta, M.

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

Dreischuh, A.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef]

Du, Y.

Du, Y.-W.

S.-Z. Pu, C.-F. Hou, K.-Y. Zhan, C.-X. Yuan, and Y.-W. Du, Opt. Commun. 285, 3631 (2012).
[CrossRef]

Dyadyusha, A.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Edmundson, D.

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

Esbensen, B. K.

B. K. Esbensen, A. Wlotzka, M. Bache, O. Bang, and W. Krolikowski, Phys. Rev. A 84, 053854 (2011).
[CrossRef]

Fattori, M.

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, Phys. Rev. Lett. 97, 250402 (2006).
[CrossRef]

Fratalocchi, A.

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

Giovanazzi, S.

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, Phys. Rev. Lett. 97, 250402 (2006).
[CrossRef]

Griesmaier, A.

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, Phys. Rev. Lett. 97, 250402 (2006).
[CrossRef]

Guo, Q.

Henninot, J. F.

Herrmann, J.

J. Herrmann, Opt. Commun. 91, 337 (1992).
[CrossRef]

Hou, C.

Hou, C.-F.

S.-Z. Pu, C.-F. Hou, K.-Y. Zhan, C.-X. Yuan, and Y.-W. Du, Opt. Commun. 285, 3631 (2012).
[CrossRef]

Kaczmarek, M.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 79, 013803 (2009).
[CrossRef]

Y. V. Kartashov and L. Torner, Opt. Lett. 32, 946 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, L. C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar and W. Krolikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

Koch, T.

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, Phys. Rev. Lett. 97, 250402 (2006).
[CrossRef]

Kong, Q.

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Phys. Rev. A 82, 013826 (2010).
[CrossRef]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Opt. Lett. 35, 2152 (2010).
[CrossRef]

Krolikowski, W.

B. K. Esbensen, A. Wlotzka, M. Bache, O. Bang, and W. Krolikowski, Phys. Rev. A 84, 053854 (2011).
[CrossRef]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Opt. Lett. 35, 2152 (2010).
[CrossRef]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Phys. Rev. A 82, 013826 (2010).
[CrossRef]

S. Skupin, M. Saffman, and W. Krolikowski, Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

Yu. S. Kivshar and W. Krolikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

Kuo, K.-H.

K.-H. Kuo, Y. Y. Lin, R.-K. Lee, and B. A. Malomed, Phys. Rev. A 83, 053838 (2011).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, L. C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Lee, R.-K.

K.-H. Kuo, Y. Y. Lin, R.-K. Lee, and B. A. Malomed, Phys. Rev. A 83, 053838 (2011).
[CrossRef]

Y. Y. Lin and R.-K. Lee, Opt. Express 15, 8781 (2007).
[CrossRef]

Lin, Y. Y.

K.-H. Kuo, Y. Y. Lin, R.-K. Lee, and B. A. Malomed, Phys. Rev. A 83, 053838 (2011).
[CrossRef]

Y. Y. Lin and R.-K. Lee, Opt. Express 15, 8781 (2007).
[CrossRef]

Liu, D.

Y. Du, Z. Zhou, H. Tian, and D. Liu, J. Opt. 13, 015201 (2011).
[CrossRef]

Malomed, B. A.

K.-H. Kuo, Y. Y. Lin, R.-K. Lee, and B. A. Malomed, Phys. Rev. A 83, 053838 (2011).
[CrossRef]

B. B. Baizakov, F. Kh Abdullaev, B. A. Malomed, and M. Salerno, J. Phys. B 42, 175302 (2009).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, L. C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, L. C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, L. C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Morandotti, R.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

Neshev, D. N.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef]

Ouyang, S.

Peccianti, M.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Pedri, P.

P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef]

Petersen, D. E.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef]

Pfau, T.

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, Phys. Rev. Lett. 97, 250402 (2006).
[CrossRef]

Pu, S.-Z.

S.-Z. Pu, C.-F. Hou, K.-Y. Zhan, C.-X. Yuan, and Y.-W. Du, Opt. Commun. 285, 3631 (2012).
[CrossRef]

Rotschild, C.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Saffman, M.

S. Skupin, M. Saffman, and W. Krolikowski, Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef]

Salerno, M.

B. B. Baizakov, F. Kh Abdullaev, B. A. Malomed, and M. Salerno, J. Phys. B 42, 175302 (2009).
[CrossRef]

Santos, L.

P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef]

Segev, M.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Skupin, S.

S. Skupin, M. Saffman, and W. Krolikowski, Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

Stuhler, J.

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, Phys. Rev. Lett. 97, 250402 (2006).
[CrossRef]

Tian, H.

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 79, 013803 (2009).
[CrossRef]

Y. V. Kartashov and L. Torner, Opt. Lett. 32, 946 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, L. C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Trillo, S.

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

Tsoy, E. N.

E. N. Tsoy, Phys. Rev. A 82, 063829 (2010).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 79, 013803 (2009).
[CrossRef]

Wang, Q.

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Opt. Lett. 35, 2152 (2010).
[CrossRef]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Phys. Rev. A 82, 013826 (2010).
[CrossRef]

Wang, Y.

Warenghem, M.

Wlotzka, A.

B. K. Esbensen, A. Wlotzka, M. Bache, O. Bang, and W. Krolikowski, Phys. Rev. A 84, 053854 (2011).
[CrossRef]

Yakimenko, A. I.

Yu. A. Zaliznyak and A. I. Yakimenko, Phys. Lett. A 372, 2862 (2008).
[CrossRef]

Yuan, C.-X.

S.-Z. Pu, C.-F. Hou, K.-Y. Zhan, C.-X. Yuan, and Y.-W. Du, Opt. Commun. 285, 3631 (2012).
[CrossRef]

Zaliznyak, Yu. A.

Yu. A. Zaliznyak and A. I. Yakimenko, Phys. Lett. A 372, 2862 (2008).
[CrossRef]

Zhan, K.-Y.

S.-Z. Pu, C.-F. Hou, K.-Y. Zhan, C.-X. Yuan, and Y.-W. Du, Opt. Commun. 285, 3631 (2012).
[CrossRef]

Zhong, W.-P.

W.-P. Zhong and M. Belić, Phys. Rev. A 79, 023804 (2009).
[CrossRef]

Zhou, Z.

J. Opt.

Y. Du, Z. Zhou, H. Tian, and D. Liu, J. Opt. 13, 015201 (2011).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

B. B. Baizakov, F. Kh Abdullaev, B. A. Malomed, and M. Salerno, J. Phys. B 42, 175302 (2009).
[CrossRef]

Nat. Phys.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Opt. Commun.

Yu. S. Kivshar and W. Krolikowski, Opt. Commun. 114, 353 (1995).
[CrossRef]

S.-Z. Pu, C.-F. Hou, K.-Y. Zhan, C.-X. Yuan, and Y.-W. Du, Opt. Commun. 285, 3631 (2012).
[CrossRef]

J. Herrmann, Opt. Commun. 91, 337 (1992).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

Yu. A. Zaliznyak and A. I. Yakimenko, Phys. Lett. A 372, 2862 (2008).
[CrossRef]

Phys. Rev. A

E. N. Tsoy, Phys. Rev. A 82, 063829 (2010).
[CrossRef]

K.-H. Kuo, Y. Y. Lin, R.-K. Lee, and B. A. Malomed, Phys. Rev. A 83, 053838 (2011).
[CrossRef]

M. Crosta, A. Fratalocchi, and S. Trillo, Phys. Rev. A 84, 063809 (2011).
[CrossRef]

W.-P. Zhong and M. Belić, Phys. Rev. A 79, 023804 (2009).
[CrossRef]

Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Phys. Rev. A 82, 013826 (2010).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 79, 013803 (2009).
[CrossRef]

B. K. Esbensen, A. Wlotzka, M. Bache, O. Bang, and W. Krolikowski, Phys. Rev. A 84, 053854 (2011).
[CrossRef]

Phys. Rev. E

D. Mihalache, D. Mazilu, F. Lederer, L. C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

Phys. Rev. Lett.

A. Griesmaier, J. Stuhler, T. Koch, M. Fattori, T. Pfau, and S. Giovanazzi, Phys. Rev. Lett. 97, 250402 (2006).
[CrossRef]

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, Phys. Rev. Lett. 102, 203903 (2009).
[CrossRef]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef]

P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef]

S. Skupin, M. Saffman, and W. Krolikowski, Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Illustration of nonlocality and competing nonlinearities on the width of dark soliton (D1): (a) D1 versus σ and α2 and (b) D1 versus σ for different values of α2. The comparison between general nonlocal (solid-curve) and weakly nonlocal (dashed-curve) solutions for (c) α2=0.1 and (d) α2=0.1, respectively.

Fig. 2.
Fig. 2.

Dynamics of dark solitons with different degrees of nonlocalities σ, for (a)–(d) focusing (α2=0.1, D1=1.09); and (e)–(h) defocusing (α2=1, D1=0.65) quintic nonlinearities. The insets show the corresponding soliton profiles at the initial (bottom) and final (top) propagation distances.

Equations (8)

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iuz+122ux2uR(xξ)|u(ξ,z)|2dξ+α2|u(x,z)|4u=0,
L=i2(u*uzuu*z)(11|u|2)12|ux|212(|u|21)R(xξ)(|u(ξ,z)|21)dξ+α23(|u|63|u|2+2).
R(x)={12σ;σxσ,0;otherwise
u(x,z)=Btanh[D(xx0)]+iA
L=L(u)dx=2dx0dz[tan1(BA)AB]23B2D+B4D[csch2(Dσ)coth(Dσ)Dσ]+α24B43D(1415B2).
coth(Dσ)Dσ[1D2σ2csch2(Dσ)]2α23D2(14B215)=13B2,
dx0dz=A[D3BBD(csch2(Dσ)coth(Dσ)Dσ)]4α2AB3D(12B25).
1D2+215σ22α2D(1415B2)=1B2.

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