Abstract

A simple but new model, an interface separated by 1-D Bessel optical potential with different modulation depth on the opposite side of the interface was proposed. We show this model can support stable surface solitons. Surface solitons form because diffraction and defocusing nonlinearity are balanced by the Bessel potential. We demonstrate numerically such solitons are stable in their entire existence domain even for higher-order Bessel potential.

© 2007 Optical Society of America

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  1. L. Stenflo, "Theory of nonlinear plasma surface waves," Physica Scripta T63, 59 (1996).
    [CrossRef]
  2. R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and nonlinear wave equations (Academic Press, London, 1982).
  3. G. Maugin, Nonlinear Waves in Elastic Crystals (Oxford University Press: Oxford, 2000).
  4. I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, "Surface multi-gap vector solitons," Opt. Express 14, 4780 (2006).
    [CrossRef] [PubMed]
  5. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete Surface Solitons," Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  6. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of Discrete Surface Solitons," Phys. Rev. Lett. 96, 063,901 (2006).
    [CrossRef]
  7. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface Gap Solitons," Phys. Rev. Lett. 96, 073,901 (2006).
    [CrossRef]
  8. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083,901 (2006).
    [CrossRef]
  9. G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, "Observation of discrete quadratic surface solitons," Opt. Express 14, 5508 (2006).
    [CrossRef] [PubMed]
  10. Y. V. Kartashov and L. Torner, "Multipole-mode surface solitons," Opt. Lett. 31, 2172 (2006).
    [CrossRef] [PubMed]
  11. K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, "Polychromatic interface solitons in nonlinear photonic lattices," Opt. Lett. 31, 3125 (2006).
    [CrossRef] [PubMed]
  12. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Surface vortex solitons," Opt. Express 14, 4049 (2006).
    [CrossRef] [PubMed]
  13. J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297 (2000).
    [CrossRef]
  14. N. Chattrapiban, E. A. Rogers, D. Cofield, W. T. Hill, and R. Roy, "Generation of non diffracting Bessel beams by use of a spatial light modulator," Opt. Lett. 28, 2183 (2003).
    [CrossRef] [PubMed]
  15. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043,902 (2005).
    [CrossRef]
  16. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton spiraling in optically induced rotating Bessel lattices," Opt. Lett. 30, 637 (2005).
    [CrossRef] [PubMed]
  17. R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, "Observation of light localization in modulated Bessel optical lattices," Opt. Express 14, 2825 (2006).
    [CrossRef] [PubMed]
  18. X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of Discrete Solitons and Soliton Rotation in Optically induced Periodic Ring Lattices," Phys. Rev. Lett. 96, 083,904 (2006).
  19. Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton Topology versus Discrete Symmetry in Optical Lattices," Phys. Rev. Lett. 95, 123,902 (2005).
    [CrossRef]
  20. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
    [CrossRef]

2006

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of Discrete Surface Solitons," Phys. Rev. Lett. 96, 063,901 (2006).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface Gap Solitons," Phys. Rev. Lett. 96, 073,901 (2006).
[CrossRef]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083,901 (2006).
[CrossRef]

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of Discrete Solitons and Soliton Rotation in Optically induced Periodic Ring Lattices," Phys. Rev. Lett. 96, 083,904 (2006).

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, "Observation of light localization in modulated Bessel optical lattices," Opt. Express 14, 2825 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Surface vortex solitons," Opt. Express 14, 4049 (2006).
[CrossRef] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, "Surface multi-gap vector solitons," Opt. Express 14, 4780 (2006).
[CrossRef] [PubMed]

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, "Observation of discrete quadratic surface solitons," Opt. Express 14, 5508 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov and L. Torner, "Multipole-mode surface solitons," Opt. Lett. 31, 2172 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, "Polychromatic interface solitons in nonlinear photonic lattices," Opt. Lett. 31, 3125 (2006).
[CrossRef] [PubMed]

2005

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043,902 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton spiraling in optically induced rotating Bessel lattices," Opt. Lett. 30, 637 (2005).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete Surface Solitons," Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton Topology versus Discrete Symmetry in Optical Lattices," Phys. Rev. Lett. 95, 123,902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
[CrossRef]

2003

2000

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297 (2000).
[CrossRef]

1996

L. Stenflo, "Theory of nonlinear plasma surface waves," Physica Scripta T63, 59 (1996).
[CrossRef]

Arlt, J.

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297 (2000).
[CrossRef]

Chattrapiban, N.

Chen, Z.

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of Discrete Solitons and Soliton Rotation in Optically induced Periodic Ring Lattices," Phys. Rev. Lett. 96, 083,904 (2006).

Christodoulides, D. N.

Cofield, D.

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
[CrossRef]

Desyatnikov, A. S.

Dholakia, K.

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297 (2000).
[CrossRef]

Egorov, A. A.

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Surface vortex solitons," Opt. Express 14, 4049 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton Topology versus Discrete Symmetry in Optical Lattices," Phys. Rev. Lett. 95, 123,902 (2005).
[CrossRef]

Ferrando, A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton Topology versus Discrete Symmetry in Optical Lattices," Phys. Rev. Lett. 95, 123,902 (2005).
[CrossRef]

Fischer, R.

Garanovich, I. L.

Hache, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of Discrete Surface Solitons," Phys. Rev. Lett. 96, 063,901 (2006).
[CrossRef]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete Surface Solitons," Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Hill, W. T.

Iwanow, R.

Kartashov, Y.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Surface vortex solitons," Opt. Express 14, 4049 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov and L. Torner, "Multipole-mode surface solitons," Opt. Lett. 31, 2172 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface Gap Solitons," Phys. Rev. Lett. 96, 073,901 (2006).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton spiraling in optically induced rotating Bessel lattices," Opt. Lett. 30, 637 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043,902 (2005).
[CrossRef]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton Topology versus Discrete Symmetry in Optical Lattices," Phys. Rev. Lett. 95, 123,902 (2005).
[CrossRef]

Kevrekidis, P. G.

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of Discrete Solitons and Soliton Rotation in Optically induced Periodic Ring Lattices," Phys. Rev. Lett. 96, 083,904 (2006).

Kivshar, Y. S.

Krolikowski, W.

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, "Observation of light localization in modulated Bessel optical lattices," Opt. Express 14, 2825 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083,901 (2006).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
[CrossRef]

Lopez-Aguayo, S.

Makris, K. G.

Malomed, B. A.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
[CrossRef]

Min, Y.

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083,901 (2006).
[CrossRef]

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083,901 (2006).
[CrossRef]

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of Discrete Surface Solitons," Phys. Rev. Lett. 96, 063,901 (2006).
[CrossRef]

Motzek, K.

Neshev, D. N.

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, "Observation of light localization in modulated Bessel optical lattices," Opt. Express 14, 2825 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083,901 (2006).
[CrossRef]

Rogers, E. A.

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083,901 (2006).
[CrossRef]

Roy, R.

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of Discrete Surface Solitons," Phys. Rev. Lett. 96, 063,901 (2006).
[CrossRef]

Schiek, R.

Siviloglou, G. A.

Sohler, W.

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of Discrete Surface Solitons," Phys. Rev. Lett. 96, 063,901 (2006).
[CrossRef]

Stegeman, G. I.

Stenflo, L.

L. Stenflo, "Theory of nonlinear plasma surface waves," Physica Scripta T63, 59 (1996).
[CrossRef]

Sukhorukov, A. A.

Suntsov, S.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of Discrete Surface Solitons," Phys. Rev. Lett. 96, 063,901 (2006).
[CrossRef]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete Surface Solitons," Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface Gap Solitons," Phys. Rev. Lett. 96, 073,901 (2006).
[CrossRef]

Y. V. Kartashov and L. Torner, "Multipole-mode surface solitons," Opt. Lett. 31, 2172 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Surface vortex solitons," Opt. Express 14, 4049 (2006).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton spiraling in optically induced rotating Bessel lattices," Opt. Lett. 30, 637 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043,902 (2005).
[CrossRef]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton Topology versus Discrete Symmetry in Optical Lattices," Phys. Rev. Lett. 95, 123,902 (2005).
[CrossRef]

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083,901 (2006).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Surface vortex solitons," Opt. Express 14, 4049 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface Gap Solitons," Phys. Rev. Lett. 96, 073,901 (2006).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043,902 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton spiraling in optically induced rotating Bessel lattices," Opt. Lett. 30, 637 (2005).
[CrossRef] [PubMed]

Wang, X.

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of Discrete Solitons and Soliton Rotation in Optically induced Periodic Ring Lattices," Phys. Rev. Lett. 96, 083,904 (2006).

Yang, H.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of Discrete Surface Solitons," Phys. Rev. Lett. 96, 063,901 (2006).
[CrossRef]

Opt. Commun.

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043,902 (2005).
[CrossRef]

X. Wang, Z. Chen, and P. G. Kevrekidis, "Observation of Discrete Solitons and Soliton Rotation in Optically induced Periodic Ring Lattices," Phys. Rev. Lett. 96, 083,904 (2006).

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton Topology versus Discrete Symmetry in Optical Lattices," Phys. Rev. Lett. 95, 123,902 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. Kartashov, L.-C. Crasovan, and L. Torner, "Stable Spatiotemporal Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 95, 023,902 (2005).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of Discrete Surface Solitons," Phys. Rev. Lett. 96, 063,901 (2006).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface Gap Solitons," Phys. Rev. Lett. 96, 073,901 (2006).
[CrossRef]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083,901 (2006).
[CrossRef]

Physica Scripta

L. Stenflo, "Theory of nonlinear plasma surface waves," Physica Scripta T63, 59 (1996).
[CrossRef]

Other

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and nonlinear wave equations (Academic Press, London, 1982).

G. Maugin, Nonlinear Waves in Elastic Crystals (Oxford University Press: Oxford, 2000).

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Figures (6)

Fig. 1.
Fig. 1.

Properties of (surface) soliton with a 0-order Bessel potential. (a) Power of surface soliton with pl = 15 and different pr versus b. (b) Profiles of ground-state soliton with pl = pr = 15. (c) Surface soliton profiles with pl = 25 and pr = 10. (d) Typical bcutoff curve versus pl for different pr .

Fig. 2.
Fig. 2.

Evolution of the solitons with (a) pl = pr = 15,b = 0.2. (b)pl = -23, pr = 16,b = 1.1. (c) pl = 8, pr = 47,b = 2.6. The white noise with variance σ2 noise = 0.01 was added into the initial input.

Fig. 3.
Fig. 3.

Properties of surfaces soliton with a 1–order Bessel potential. (a) Power of surface soliton with pl = 15 and different pl versus b. (b) Typical bcutoff curves with pl for different pr .

Fig. 4.
Fig. 4.

Profiles of surface soliton with 1-order Bessel potential. (a) pl = pr = 15,b = 1.6, (b) pl = -5, pr = 25,b = 0.8, (c) pl = -5, pr = 2,b = 0.05, (d) pl = 2, pr = 35,b = 0.5

Fig. 5.
Fig. 5.

Evolution of the solitons shown in Fig. 4. The white noise with variance σ2 noise = 0.01 was added into the initial input.

Fig. 6.
Fig. 6.

Profiles and evolution of the solitons with higher-order Bessel potential. (a,d) pl = pr = 20,b = 0.2, (b,e) pl = 10, pr = 20,b = 0.5 with n = 2. (c,f) pl = 100, pr = 250,b = 1.8 with n = 5. The white noise with σ2 noise = 0.01 was added into the initial input in (d,e,f).

Equations (5)

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i A z + 1 2 2 A x 2 A 2 A + R ( x ) A = 0
P = A 2 dx H = 1 2 [ dA dx 2 2 R ( x ) A 2 + A 4 ] dx
d 2 q dx 2 2 bq 2 q 3 + 2 Rq = 0
λu = 1 2 d 2 u dx 2 q 2 ( 2 u + v ) + Ru bu
λv = 1 2 d 2 v dx 2 + q 2 ( 2 u + v ) Rv + b v

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