Abstract

We derive analytical bright and dark similaritons of the generalized coupled nonlinear Schr¨odinger equations with distributed coefficients. An exact balance condition between the dispersion, nonlinearity and the gain/loss has been obtained. Under this condition, we discuss the nonlinear similariton tunneling effect.

© 2010 Optical Society of America

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  1. A. Hasegawa, and F. Tappet, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23, 142–170 (1973).
    [CrossRef]
  2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and soliton in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
    [CrossRef]
  3. G. P. Agrawal, Nonlinear Fiber Optics, (New York: Academic Press, 1993).
  4. C. G. L. Tiofacka, A. Mohamadoub, T. C. Kofane, and K. Porsezian, “Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled nonlinear Schrödinger equations,” J. Mod. Opt. 57, 261–272 (2010).
    [CrossRef]
  5. V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056619 (2005).
  6. V. I. Kruglov, and J. D. Harvey, “Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters,” J. Opt. Soc. Am. B 23, 2541–2550 (2006).
    [CrossRef]
  7. C. Q. Dai, Y. Y. Wang, and J. F. Zhang, “Analytical spatiotemporal localizations for the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Opt. Lett. 35, 1437–1439 (2010).
    [CrossRef]
  8. A. C. Newell, “Nonlinear tunneling,” J. Math. Phys. 19, 1126–1133 (1978).
    [CrossRef]
  9. V. N. Serkin, and T. L. Belyaeva, “High-energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).
    [CrossRef]
  10. J. F. Wang, L. Li, and S. T. Jia, “Nonlinear tunneling of optical similaritons in nonlinear waveguides,” J. Opt. Soc. Am. B 25, 1254–1260 (2008).
    [CrossRef]
  11. R. C. Yang, and X. L. Wu, “Spatial soliton tunneling, compression and splitting,” Opt. Express 16, 17759–17767 (2008).
    [CrossRef]
  12. L. Li, Z. H. Li, S. Q. Li, and G. S. Zhou, “Modulation instability and soliton on cw background in inhomogeneous optical fiber media,” Opt. Commun. 234, 169–176 (2004).
    [CrossRef]

2010 (2)

C. G. L. Tiofacka, A. Mohamadoub, T. C. Kofane, and K. Porsezian, “Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled nonlinear Schrödinger equations,” J. Mod. Opt. 57, 261–272 (2010).
[CrossRef]

C. Q. Dai, Y. Y. Wang, and J. F. Zhang, “Analytical spatiotemporal localizations for the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Opt. Lett. 35, 1437–1439 (2010).
[CrossRef]

2008 (2)

2006 (1)

2005 (1)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056619 (2005).

2004 (1)

L. Li, Z. H. Li, S. Q. Li, and G. S. Zhou, “Modulation instability and soliton on cw background in inhomogeneous optical fiber media,” Opt. Commun. 234, 169–176 (2004).
[CrossRef]

2001 (1)

V. N. Serkin, and T. L. Belyaeva, “High-energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).
[CrossRef]

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and soliton in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

1978 (1)

A. C. Newell, “Nonlinear tunneling,” J. Math. Phys. 19, 1126–1133 (1978).
[CrossRef]

1973 (1)

A. Hasegawa, and F. Tappet, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23, 142–170 (1973).
[CrossRef]

Belyaeva, T. L.

V. N. Serkin, and T. L. Belyaeva, “High-energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).
[CrossRef]

Dai, C. Q.

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and soliton in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Harvey, J. D.

V. I. Kruglov, and J. D. Harvey, “Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters,” J. Opt. Soc. Am. B 23, 2541–2550 (2006).
[CrossRef]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056619 (2005).

Hasegawa, A.

A. Hasegawa, and F. Tappet, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23, 142–170 (1973).
[CrossRef]

Jia, S. T.

Kofane, T. C.

C. G. L. Tiofacka, A. Mohamadoub, T. C. Kofane, and K. Porsezian, “Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled nonlinear Schrödinger equations,” J. Mod. Opt. 57, 261–272 (2010).
[CrossRef]

Kruglov, V. I.

V. I. Kruglov, and J. D. Harvey, “Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters,” J. Opt. Soc. Am. B 23, 2541–2550 (2006).
[CrossRef]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056619 (2005).

Li, L.

J. F. Wang, L. Li, and S. T. Jia, “Nonlinear tunneling of optical similaritons in nonlinear waveguides,” J. Opt. Soc. Am. B 25, 1254–1260 (2008).
[CrossRef]

L. Li, Z. H. Li, S. Q. Li, and G. S. Zhou, “Modulation instability and soliton on cw background in inhomogeneous optical fiber media,” Opt. Commun. 234, 169–176 (2004).
[CrossRef]

Li, S. Q.

L. Li, Z. H. Li, S. Q. Li, and G. S. Zhou, “Modulation instability and soliton on cw background in inhomogeneous optical fiber media,” Opt. Commun. 234, 169–176 (2004).
[CrossRef]

Li, Z. H.

L. Li, Z. H. Li, S. Q. Li, and G. S. Zhou, “Modulation instability and soliton on cw background in inhomogeneous optical fiber media,” Opt. Commun. 234, 169–176 (2004).
[CrossRef]

Mohamadoub, A.

C. G. L. Tiofacka, A. Mohamadoub, T. C. Kofane, and K. Porsezian, “Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled nonlinear Schrödinger equations,” J. Mod. Opt. 57, 261–272 (2010).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and soliton in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Newell, A. C.

A. C. Newell, “Nonlinear tunneling,” J. Math. Phys. 19, 1126–1133 (1978).
[CrossRef]

Peacock, A. C.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056619 (2005).

Porsezian, K.

C. G. L. Tiofacka, A. Mohamadoub, T. C. Kofane, and K. Porsezian, “Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled nonlinear Schrödinger equations,” J. Mod. Opt. 57, 261–272 (2010).
[CrossRef]

Serkin, V. N.

V. N. Serkin, and T. L. Belyaeva, “High-energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and soliton in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Tappet, F.

A. Hasegawa, and F. Tappet, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23, 142–170 (1973).
[CrossRef]

Tiofacka, C. G. L.

C. G. L. Tiofacka, A. Mohamadoub, T. C. Kofane, and K. Porsezian, “Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled nonlinear Schrödinger equations,” J. Mod. Opt. 57, 261–272 (2010).
[CrossRef]

Wang, J. F.

Wang, Y. Y.

Wu, X. L.

Yang, R. C.

Zhang, J. F.

Zhou, G. S.

L. Li, Z. H. Li, S. Q. Li, and G. S. Zhou, “Modulation instability and soliton on cw background in inhomogeneous optical fiber media,” Opt. Commun. 234, 169–176 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

A. Hasegawa, and F. Tappet, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. anomalous dispersion,” Appl. Phys. Lett. 23, 142–170 (1973).
[CrossRef]

J. Math. Phys. (1)

A. C. Newell, “Nonlinear tunneling,” J. Math. Phys. 19, 1126–1133 (1978).
[CrossRef]

J. Mod. Opt. (1)

C. G. L. Tiofacka, A. Mohamadoub, T. C. Kofane, and K. Porsezian, “Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled nonlinear Schrödinger equations,” J. Mod. Opt. 57, 261–272 (2010).
[CrossRef]

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

JETP Lett. (1)

V. N. Serkin, and T. L. Belyaeva, “High-energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).
[CrossRef]

Opt. Commun. (1)

L. Li, Z. H. Li, S. Q. Li, and G. S. Zhou, “Modulation instability and soliton on cw background in inhomogeneous optical fiber media,” Opt. Commun. 234, 169–176 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056619 (2005).

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and soliton in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, (New York: Academic Press, 1993).

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