Abstract

By means of direct simulations and theoretical analysis, we study the nonlinear propagation of truncated Airy pulses in an optical fiber exhibiting both anomalous second-order and strong positive third-order dispersions (TOD). It is found that the Airy pulse first reaches a finite-size focal area as determined by the relative strength of the two dispersion terms, and then undergoes an inversion transformation such that it continues to travel with an opposite acceleration. The system notably features tight focusing if the TOD is a dominant factor. These effects are partially reduced by Kerr nonlinearity.

© 2013 Optical Society of America

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  1. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  2. J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
    [CrossRef]
  3. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
    [CrossRef]
  4. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
    [CrossRef]
  5. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
    [CrossRef]
  6. I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
    [CrossRef]
  7. N. K. Efremidis, Opt. Lett. 36, 3006 (2011).
    [CrossRef]
  8. Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, Opt. Lett. 37, 3201 (2012).
    [CrossRef]
  9. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef]
  10. P. Saari, Opt. Express 16, 10303 (2008).
    [CrossRef]
  11. I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, Opt. Express 19, 23132 (2011).
    [CrossRef]
  12. P. Piksarv, H. Valtna-Lukner, A. Valdmann, M. Lõhmus, R. Matt, and P. Saari, Opt. Express 20, 17220 (2012).
    [CrossRef]
  13. Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. R. Driben, F. Mitschke, and N. Zhavoronkov, Opt. Express 18, 25993 (2010).
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    [CrossRef]

2013 (2)

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
[CrossRef]

R. Driben, B. A. Malomed, A. V. Yulin, and D. V. Skryabin, Phys. Rev. A 87, 063808 (2013).

2012 (6)

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

P. Piksarv, H. Valtna-Lukner, A. Valdmann, M. Lõhmus, R. Matt, and P. Saari, Opt. Express 20, 17220 (2012).
[CrossRef]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, Opt. Lett. 37, 3201 (2012).
[CrossRef]

R. Driben and I. Babushkin, Opt. Lett. 37, 5157 (2012).
[CrossRef]

2011 (8)

2010 (3)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

R. Driben, F. Mitschke, and N. Zhavoronkov, Opt. Express 18, 25993 (2010).
[CrossRef]

2009 (2)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

2008 (3)

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

I. M. Besieris and A. M. Shaarawi, Phys. Rev. E 78, 046605 (2008).
[CrossRef]

P. Saari, Opt. Express 16, 10303 (2008).
[CrossRef]

2007 (2)

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

1991 (1)

B. A. Malomed, Phys. Rev. A 43, 3114 (1991).
[CrossRef]

1979 (1)

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Ament, C.

C. Ament, P. Polynkin, and J. V. Moloney, Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

Amiranashvili, S.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

Arie, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Azaña, J.

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
[CrossRef]

Babushkin, I.

Baronio, F.

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Besieris, I. M.

I. M. Besieris and A. M. Shaarawi, Phys. Rev. E 78, 046605 (2008).
[CrossRef]

Bongiovanni, D.

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
[CrossRef]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, Opt. Lett. 37, 3201 (2012).
[CrossRef]

Brée, C.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chen, Z.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, Opt. Express 19, 23132 (2011).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

Clerici, M.

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
[CrossRef]

Conforti, M.

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

Degasperis, A.

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

Demircan, A.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Driben, R.

Efremidis, N. K.

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Fattal, Y.

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Hu, Y.

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
[CrossRef]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, Opt. Lett. 37, 3201 (2012).
[CrossRef]

Janunts, N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Kaminer, I.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, Opt. Express 19, 23132 (2011).
[CrossRef]

Kivshar, Y. S.

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, Opt. Lett. 36, 1164 (2011).
[CrossRef]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Klein, A. E.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Li, M.

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
[CrossRef]

Liu, W.

Liu, Y.

Lõhmus, M.

Lou, C.

Lu, C.

Lumer, Y.

Mahnke, C.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

Malomed, B. A.

R. Driben, B. A. Malomed, A. V. Yulin, and D. V. Skryabin, Phys. Rev. A 87, 063808 (2013).

B. A. Malomed, Phys. Rev. A 43, 3114 (1991).
[CrossRef]

Marom, D. M.

Matt, R.

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Minovich, A.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Miroshnichenko, A. E.

Mitschke, F.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

R. Driben, F. Mitschke, and N. Zhavoronkov, Opt. Express 18, 25993 (2010).
[CrossRef]

Miyagi, M.

Moloney, J. V.

C. Ament, P. Polynkin, and J. V. Moloney, Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Morandotti, R.

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
[CrossRef]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, Opt. Lett. 37, 3201 (2012).
[CrossRef]

Nemirovsky, J.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Neshev, D. N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, Opt. Lett. 36, 1164 (2011).
[CrossRef]

Nishida, S.

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Pertsch, T.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Piksarv, P.

Polynkin, P.

C. Ament, P. Polynkin, and J. V. Moloney, Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Rudnick, A.

Saari, P.

Segev, M.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, Opt. Express 19, 23132 (2011).
[CrossRef]

Shaarawi, A. M.

I. M. Besieris and A. M. Shaarawi, Phys. Rev. E 78, 046605 (2008).
[CrossRef]

Shadrivov, I. V.

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

Skryabin, D. V.

R. Driben, B. A. Malomed, A. V. Yulin, and D. V. Skryabin, Phys. Rev. A 87, 063808 (2013).

Song, D.

Steinmeyer, G.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

Sun, Z.

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Valdmann, A.

Valtna-Lukner, H.

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Wabnitz, S.

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

Wang, S.

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Xu, J.

Yao, J.

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
[CrossRef]

Yin, X.

Yulin, A. V.

R. Driben, B. A. Malomed, A. V. Yulin, and D. V. Skryabin, Phys. Rev. A 87, 063808 (2013).

Zhang, P.

Zhang, X.

Zhavoronkov, N.

Appl. Opt. (1)

Nat. Photonics (3)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Opt. Express (5)

Opt. Lett (1)

Y. Hu, M. Li, D. Bongiovanni, M. Clerici, J. Yao, Z. Chen, J. Azaña, and R. Morandotti, Opt. Lett 38, 380 (2013).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (2)

R. Driben, B. A. Malomed, A. V. Yulin, and D. V. Skryabin, Phys. Rev. A 87, 063808 (2013).

B. A. Malomed, Phys. Rev. A 43, 3114 (1991).
[CrossRef]

Phys. Rev. E (1)

I. M. Besieris and A. M. Shaarawi, Phys. Rev. E 78, 046605 (2008).
[CrossRef]

Phys. Rev. Lett. (7)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

C. Ament, P. Polynkin, and J. V. Moloney, Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Sci. Rep. (1)

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Dynamics of Airy pulses under the dominant action of TOD, with ε=1000 in Eq. (1). The truncation is a=0.1 in (a) and 0.01 in (b). Here and below, all results are presented in normalized units.

Fig. 2.
Fig. 2.

Dynamics of the truncated Airy pulse under the combined action of second- and third-order dispersions with comparable strengths, ε=0.5 in Eq. (1). The truncation parameter is a=0.01.

Fig. 3.
Fig. 3.

(a) Minimal scaled TOD coefficient, necessary for the occurrence of the reversal transformation, versus the truncation parameter of the initial Airy pulse, a. (b) Size of the focal area versus the TOD coefficient, at fixed a=0.01.

Fig. 4.
Fig. 4.

Dynamics of the truncated Airy pulse under the combined action of the second- and third-order dispersions, as predicted by Eqs. (3) and (4), for ε=1 and a Gaussian-truncation parameter α=0.02. Inset: intensity profile at the focal point. The solid blue line is produced by Eq. (4), while the red curve marked by circles represents direct simulations of Eq. (1).

Fig. 5.
Fig. 5.

Dynamics of the Airy pulse in the nonlinear regime (a) under the prevalence of TOD [ε=1000, as in Fig. 2(b)], with A0=3, and (b) under the combined action of second- and third-order dispersions with comparable strengths (ε=1, as in Fig. 4, with A0=5), featuring the generation of multiple solitons. The truncation parameter is a=0.01.

Equations (4)

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iφξ+(1/2)sgn(β2)φTT(1/6)iεφTTT+|φ|2φ=0,
ψξ=(i/2)sgn(β2)ω2ψ+(i/6)εω3ψ.
|φ(ξ,T)|2=2πθ2/3|Ai[θ1/3(T+14θξ2α2θ+isgn(β2)αθξ)]|2×exp(2αθT+4α33θ2θ2αξ2),
|φ(T)|2=12α2+1/ε2exp(T22α+2/(αε2)).

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